First off, you don't lift decals from the backing, you will actually lift the wax paper backing up also doing that, and it will stick to the back of your decal. You squeegee the decal front transfer tape, real good, then turn the decal face down and slowly peel the backing away from the decal. It makes a huge difference. I actually write this on every decal that I sell. I use Main ( NEKOOSA) medium tack paper tape, and have for many years. No problems or complaints. I sell some very large and detailed designs. I had to look that tape up MT80P. Paper tape is the way to go. Not that clear stuff. You cannot, roll, bend ,stretch or use the MT80P wet. Pros use paper tape.
Another problem, could be that your cutting too deep and pushing the vinyl into the backing. Possibly you are using the wrong blade depth instructions that are out there. . Never use instructions that use a credit card or post it notes for setting blade depth. This is the correct way to set your blade depth.
To start with, you should set your blade depth correctly, by taking the blade holder out of the machine, and firmly cut across a piece of scrap vinyl, you will be cutting. You should only be cutting the vinyl and barely a mark on wax paper backing, Adjust blade to get there, Then put the blade holder back in machine, and use the force of the machine to get there, same results, only cutting the vinyl and barely a mark in wax paper backing. You should just barely see and feel your blade tip out of the blade holder.
The transfer tape that I use is very similar to this. I have bought mine from another dealer for many years now, closer to me.
https://www.uscutter.com/Main-Tape-GXP750-PerfecTear-Plus-Medium-Tack-Transfer-Tape