I've just cut a section of acrylic tube...I mark the cut line with a wrap of masking tape, then cut round the edge slowly with a small hacksaw with a brand new blade fitted. Keep going round and round, every now and again I add a drop of warm water with washing up liquid mixed in it, and you should end up with a nice clean cut.
Just a cheap pound store hacksaw.
I then go over the cut edge with a long file to give me a level edge all round, then finish off by attaching a fresh sheet of coarse wet 'n dry paper to a sheet of glass and rub the cut edge down smooth. To complete the job, I rub the edge down once more with fine wet 'n dry paper, then rinse the finished tube under the tap to clean out the dust. Dry with a tissue...job done.