Never be pulling from the roll while cutting. Always have enough vinyl slack to do the order. You may have your blade too far out of the blade holder, with will cause the vinyl to shift. This is how to set your blade depth correctly. Run the cutter slow until you learn it. Vinyl has to be straight to stay straight while traveling. I have a Graphtec, but I still run it slow.
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 fell the blade tip out of the blade holder.
A lot of the times when a cutter stops, it is static from the vinyl. Cutter must be grounded to the stand. Spray Static Guard type sprays, use dryer sheets on the cutter and inside the roll. Run humidifier. Also the MH cutters have a very limited memory. The value cutters do have a cheap Chinese chip set. We tell buyers to put it on a serial cable or a Tripp-Lite Keyspan Adpater. That is the brand name Tripp-LIte.