i've cut all kinds of stuff that were unconventional to see for myself...I bet it can be done, tho' you would need a backer...and i bet if you have some wax paper from vinyl sign material you could use it for a backer..tho' i would want to make sure the edges of your tape werent lifting to jam in your cutter.
Adjust the speed and downforce..
edit: you would need a heavy downforce... what does the Sitka do?