If you go with double stick tape you need to make sure both surfaces are clean of dust. I don't recommend carpet tape because of cleanup issues. I use what they call turners tape, it is made with crape paper and special adhesives that usually come off clean. The plastic bond side there would not be any problem with, it is the bed side that you need to make sure it is flat and clean. I use it on small parts when I am cutting them out of small pieces that have little or no clamping area. I have never had a problem with it coming loose. I also use it for template routing.
If I were doing a lot of plastic routing I would make a small vacuum system that fit the project I would be cutting.