1. One trick to cutting cheesecake neatly is keeping the knife (a very sharp knife) in use clean and smooth.
2. To do this, fill a tall container with hot tap water deep enough to cover the blade of your knife.
3. Dip the knife into the hot water, then wipe clean on a clean towel before making every cut.
4. The constant dipping and cleaning will prevent chunks of cake from previous chunks of cake from previous slice from depositing on top of the next slice.
Good luck :)