Although the above video is not really the best intro into making your own laser cutter, it does make sense -- right? Take apart a few household PC scanners with stepper motors intact, modify them as shown in these documented steps and see if you can turn those parts into a custom laser cutter with some computer code know-how for specific directions to send to the motors that control the lasers.
Since scanners are basically laser readers anyway (like any CD or DVD player), this makes sense -- but it's doubtful the laser cutter made in this video has the power to cut much else then paper or other soft materials. Still, if you try this, let us know if you can chop that cinder block in half, okay?
Cost varies, but should be around $30 in parts given you have a few broken or unused scanners laying around. The basic components needed for this project include a few laser diodes, some aluminum rods, brass brackets and a breadboard to get everything connected.