I've turned some "chippy" acrylics before, like "Pot of Gold" and some of the other plastic blanks from PSI...
Michael has some good tips there, regarding the use of a carbide cutter .... approach the material dead on center with a negative rake angle and scrape away, after you get it pretty much rounded, and be careful around the edges of the blank. If it's still popping little divots into it once you get reasonably close to your final diameter, switch to wet-sanding with 150 or 220 grit paper on a wooden backer board to keep things reasonably squared up.
There's no shame in giving up your chisel if it just can't do the job with your level of skill ... after all, the objective is to get the job done no matter what you have to do. Once it's all done and finished and everybody's admiring the job you did, feel free to lie your butt off and tell us you did it all with the skew (or your tool of choice)! It's not like we were there to watch you through your trials and tribulations, lol!