i suppose it would work, if your plastics are opaque to IR (and the specific wavelength of your laser).
though 1W wouldn't really cut much. you would need to spend big $$$ to get a laser that could happily cut through thick acrylics, assuming they are NOT transperant to the wavelenghth of the laser you are using.
a CO2 laser should do the job, but then you are looking at a lot more than $250, unless you build one http://www.repairfaq.org/sam/lasercc2.htm
well I sell 1 and 2 watt IR portables (just click on the blaze lasers ad, its my shop) for much better prices than that.
I have one of each coming shortly so I'd be happy to test it on acrylic.
I also have an old X-Y plotter that I plan to convert to a X-Y laser cutter with maybe a 2 watt diode.
A 1 or 2 watt can cut or melt just about anything it is pointed at, that absorbs IR. Whether or not it can cut something transparent is another thing.
Not many materials are transparent to IR light so most plastics will propably cut well.
Be aware that certain types of plastic emit VERY toxic fumes when heated or burned so read up before and always use adequate fume extraction.
Anybody can tell me if I should get a Destructive gear laser or Blaze laser, and if Blaze Red or green? I want to pop balloons and light matches and cigarettes.