There are many ways to answer that question: biblically, theologically, historically, and socially. I'll attempt to come at it at every angle mentioned above in reverse order.
1. Socially we must speak of "heresy" as division, since that is really from whence the term comes. Preterism certainly has caused major divisions in its aggressiveness to undermine all other eschatological systems. In this way, it seems as though it cannot tolerate other systems well, and indeed, must continually assert itself over more important matters of faith. Indeed, it seems to become a core doctrine of the faith for many Preterists as it consumes much of their time and energy. Often, Preterists would rather end whole churches than cease and desist from making it an issue. For this reason, it can be a social heresy (but, of course, many things can be in this sense).
2. Historically, all eschatological positions are in line with what Christians have declared in the creeds. All except one that is: Preterism. Because of its denial of the Second Coming of Christ in the flesh, the bodily resurrection (i.e., that this earthly body will be redeemed and transformed), the future judgment, etc., it sets itself up against the creeds and what "all Christians everywhere" have believed within the historic orthodox Christian Church. It flies in the face, in fact, of the early Apostle's Creed upon which almost all subsequent creeds are based. For this reason, it is a historical heresy.
3. Theologically, Preterism undermines core doctrines of the Christian faith that have to do with the nature of man and sometimes even that of Christ. It must posit the gnostic idea that man is merely a spirit clothed in flesh rather than an inspirited physical creature made up of body and spirit intermingled. This distorts all humans, what is saved by Christ, and Christ's nature as well, since Christ's body would merely be a shell as well, and not make up a major element of who He is (i.e., a denial of His human nature in terms of what makes up the human nature). It also denies what the gospel accomplishes (what Christ gains for Himself is gained for us, but what is not gained for Himself cannot be obtained by us, i.e., a different body or a state of existence as spirits). There is simply a profound misunderstanding of the gospel in Preterism. One might say that Preterism only denies these by a logical entailment that is only sometimes, but not always, pursued to the fullest by Preterists; but this would merely be walking the line much like other heretical views that are rejected by the church more for what they imply than what is explicitly affirmed. For this reason, Preterism is a theological heresy.
Finally, and perhaps, most importantly, we come to whether it is a biblical heresy. Apart from what can be inferred from above, there are two key passages that may help us answer this question.
The first is a commonly discussed passage by both sides:
2 Timothy 2:16-19:
But stand clear of godless foolish talk, for it will lead to further ungodliness, and their talk will spread like gangrene. Among them are Hymenaeus and Philetus, [men] who have gone astray from the truth saying that the resurrection has already taken place, and they upset the faith of some. Nevertheless, the firm foundation of God stands, having this seal, "The Lord knows those who are His," and, "Everyone who names the name of the Lord is to abstain from wickedness."
Some observations here:
a. Paul calls this ungodly and cancer.
b. He states that those who teach this have gone astray from the truth.
c. He seems to suggest that those who teach this do not belong to God in contrast to those who are known by the Lord.
Now, what is this teaching that states the resurrection had already occurred?
Preterists like to argue that this proves that the resurrection must have been seen as a spiritual event, since the heretics are able to argue this way and convince people that it had already taken place.
Whereas this is an interesting deflection, what seems to escape their notice is that the more likely interpretation in a proto-gnostic context is that these heretics were spiritualizing the physical resurrection and arguing that it had already taken place. This follows the pattern of those who deny that Jesus is coming in the flesh, which brings me to the other passage that is not so well discussed.
2 John 1:7:
Many translations simply get this text wrong, and thus, it is widely unknown to most Preterists. The assumption seems to be that John is talking about the same thing he was talking about in 1 John, i.e., that Jesus had come in the flesh (i.e., physically as opposed to spiritually in the way the Docetic Gnostics argued).
However, one must remember that these letters don't provide the context for one another, as they are different written works. They may provide some context to the author's overall thinking, but they need to be read as distinct works first.
This brings us to an important point. In 1 John, John uses the Perfect or Aorist to refer to Christ's incarnation and earthly ministry, never the Present.
In this verse, however, John uses the Present Participle ἐρχόμενον. In a colossal mistake, most translations translate them the same, likely due to confusing the phrase with the Perfect Participle in 1 John 4:2 and 5:6, but in fact, they are not the same. The Present Participle is used to refer to Christ's Coming in the Synoptics, i.e., "is coming" (Matt 16:28; 24:30; 26:64; Mark 13:26; 14:62; Luke 21:27).
Hence, in the Greek, the text reads:
For many deceivers have gone out into the world, those who do not acknowledge Jesus Christ is coming in the flesh. This is the deceiver and the antichrist. Watch yourselves, that you do not lose what we have accomplished, but that you may receive a full reward. Anyone who goes too far and does not abide in the teaching of Christ, does not have God; the one who abides in the teaching, he has both the Father and the Son. If anyone comes to you and does not bring this teaching, do not receive him into [your] house, and do not give him a greeting; for the one who gives him a greeting participates in his evil deeds.
Notice, the one who denies that Christ is coming in the flesh is a deceiver and antichrist, one who will not receive a full reward, and who does not have God. He is not to be received into the church or even greeted. So whatever this is, it is an example of heresy, and it has to do with not confessing that Jesus Christ is coming in the flesh.
To bring back a statement from 1 John, "when He appears we will be like Him," Christ must actually appear (a word that describes one making oneself physically visible) in order for us to be made like Him (and as I argued before, this refers to our physical bodies).
Hence, it is probable that John is saying that a failure to confess that Jesus is coming in the flesh/physically, and to argue that He returns spiritually in some way, not merely in micro-events that foreshadow the macro, but as the only macro event itself, is to be of the deceiver and antichrist (i.e., replacing Christ and His work with another christ and another work). For this reason, Preterism is a biblical heresy.
The issue at this point becomes one where we discuss how we deal with individuals who have fallen into this, or any, heresy in love. A thorough effort to teach the teachable should be made with blood, sweat, and tears. Lots of prayer for the individuals and lots of conversations to make sure that they are not simply deceived sheep who need to be led to less polluted waters. Love for God, the purity of His flock, and then the individuals who have gone astray should be our motivating influence in that order.
The charge of heresy also should not replace a thoughtful dialogue in seeking this reconciliation, as many have sought to use it as an ad hominem rather than engage in serious conversation.
However, once it is evident that they are dug in and not going to be teachable anymore, it is then that John's instruction becomes relevant, and we, sadly, must move on from them and withdraw the hand of fellowship, as the Apostle commands.