Hi,
Ultrasonics are used to 'weld' plastic but that's because the plastic vibrates and rubs on the joining piece and that creates heat which then melts the plastic in only the area that is touching.
Another way to cut plastic is with a Dremel. There are various cutting bits and disks you can buy, but you can make a much better one yourself quite easily. Take one of the 'saw blades' they sell for the Dremel and grind all the teeth off of it with a grinding wheel. These are the very thin metal saw blades that are used at the end of a mandrel (screwed on the end). The teeth are no good to keep on there as they keep grabbing the work. So without the teeth you essentially have a disk that rotates, rotates at high speed and when it touches the plastic it melts it, but melts only a tiny width of material, so even long cuts dont smell. The amount of material that is removed in order to make the cut is very very small too, almost negligible, less than 1/32 of an inch. The edges need cleaning up a little after the cut but it's not difficult only taking a minute or less.
I suppose you can make one out of a steel washer too, but that would be thicker than the Dremel saw blades they sell for the mandrel. They are extremely thin and make a nice cut when they have no teeth. The teeth might be ok for wood but not for plastic, and even in wood they keep grabbing the material and the Dremel tries to jerk out of your hand. Note that these are not the saw blades they sell for their special saw blade attachement whcih are bigger and bulky and quite thick (maybe 1/16 inch or thicker). The thin ones (with no teeth) that screw onto the end of a mandrel work best.
I've cut quite a bit of plastic with this kind of home made (partly home made anyway) saw blade. Plexiglass, ABS, etc., and i've done some long cuts this way too with a curvy cut pattern so curved cuts work too. Max thickness maybe 1/4 inch or less. 1/8 inch thick plastic goes fast, the thicker takes longer. If it is too thick then it requires cutting on both sides but that's not too easy to do.