If you are talking about a dress shirt, the bottom of the back is actually called the "tail" or "shirttail":
There is a cut in my shirttail.
The 'bottom' of most garments is called "the hem", or possibly "the fringe" (the latter is a little old-fashioned), so you could say:
There is a cut in the hem of my shirt, at the back.
"Top left", and "bottom right" etc are idiomatic, but the words "back" and "front" aren't usually used that way because they describe the whole surface, not just a part of it. If you must describe the location of the cut I would say the most natural way would be:
There is a cut at the bottom of my shirt, on the back.