Can you cut acrylic with a table saw (universal wood blade)? Or is this a very bad idea, as it will badly melt the acrylic and make a mess of everything; or dull the blade or something like that?
Universal wood blade might not be the best for this. Blades with a high tooth count (100 or more for a 10" blade) will work best. Try to find a blade with a low rake angle (teeth should look straighter rather than laying down at an angle). Blade height should be adjusted so the blade sticks above the material 1/2 or more rather than just clearing the material as is common with wood.
For thinner material, you want very tight clearance between the blade and the throat plate. This helps prevent chipping because the material is supported as much as possible. This might mean making a custom throat plate or buying a low clearance plate made for your saw.
Your fence needs to be strait and sturdy, and again for thin material make sure theres not a gap under the fence where the material can slide.
It could work if you do everything just right. Hold it securely so it can't chatter, move it through at just the right speed, and make sure to keep tight to the fence during the entire cut.
If you go too slowly it will melt, leaving you with gobs of plastic on the edges of your cut. If you go too quickly you'll shatter it. The only way to know for sure with your saw and your blade and your skills is to give it a try.