Details of how to make a burning laser have appeared repeatedly here on Instructables.Details of how to make a CNC milling platform have also appeared repeatedly here on Instructables.Put the lime in the coconut.
(And be careful. Any laser powerful enough to cut is powerful enough for a stray reflection to damage your eyes in an instant.)
You can, but the industrial cutters use 10-50 watt lasers capable of cutting ...lots... a dvd or blu-ray burner can SLOWLY cut opaque materials...at much much less than 1 watt... the principal is the same, just MUCH slower and smaller.
For cutting what? L