How much can you slice off an MDF door?
The answer depends on whether it is hollow or solid. If it is hollow then you need to find out how much is solid on each end. If it is solid then there is no issue. For example, taking one door somewhat randomly from Home Depot based on Interior Door + Hollow Core + not pre-hung: 



This one is hardwood rather than MDF, but that really shouldn't matter much. What matters is the specifications from the manufacturer for the specific door. In this case:


  Door trimmable for custom fit up to 1/4in T, 3/4in B &amp; 1/8in S


If it is solid then you can trim as much as you want, but you pay a lot more for the door.