Use double-sided tape or carpet tape to secure your thin 1/16" acrylic board to the waste board. This works better than trying to clamp down the acrylic as tabs are not practical with such thin material.
Acrylic requires the right speed for milling as too fast will melt the acrylic, build on the end mill and interfere with the carving. And too slow will cause chipping and may cause the acrylic to crack.
I’ve found the slowest speed, 1 @ approximately 16,000 RPM, on the Dewalt DWP611 works well.