The microwave will come down, unless all of the cabinet trim was installed after the microwave went in. Even then it "should" be possible to get it out.
I'm assuming that you have a small cabinet above the microwave. If no does it vent straight into plumbing in the attic? You should be able to get up there and remove/disconnect the vents up there.
If there's a small gap above the microwave, between it and the cabinet trim, disconnect the vent plumbing, and gently push up on the microwave. The last one that I hung had a steel plate on the wall with tabs that the microwave clipped into. You can probably google the original installation instructions for your model.