Yes. Depends on how good you are at sewing. ponts to bear in mind: the T shirt fabric will stretch like blazes once it as been cut, and machine stitching doesn't alwyas work well - again because of the stretchiness - so hand-stitching might give a better result.
If you want a very punk look, just cut the fabric and don't bother with any stictching to finish off.
Draw a chalk line where you want your new neckline to be - then cut 'north' of this line ie leaving extra fabric near your neck. This you will see is because as soon as the crew neck band is cut off, the T shirt starts to stretch.
The fabric doen't run into holes like ladies tights - at least, not easily - so no worries if you just leave it lke that.
To make a finished neck, make a tiny neat rolled hem.
This is what i mean about the process depnding on how well you can sew.