How to secure acrylic 1/16" not damage

I want to secure acrylic 1/16" and try to add double tape or carpet tape , not succeeded and damage the project.
any help or succeed .

Apply painters tape to your machine bed.
Apply painters tape to the backside of your workpiece.
Glue the workpiece tape to the machine bed tape with CA glue.

When done carving, remove the tape.