There are two potential problems parting acrylic. One is that if the tool has any top rake it will tend to dig in, actually on small diameters to acrylic will tend to climb up onto the tool. The second problem is the chips getting stuck in the groove, getting hot and soft and tending to weld back onto the sides of the groov again causing it to ride up. The welding effect is exacerbated with extruded acrylic.
Try using a freshly sharpened HSS parting tool with zero top rake, even a little bit of negative rake and lubricate it with a bit of soap solution.