KevinC has the right answer - use either a dedicated set of cable cutting pliers from a bike manufacturer (don't use regular pliers or regular cable cutters, they will crush the housing) or use a dremel tool.
If using a cable cutting tool, make sure to either use a deburring tool to remove the sharp edges. Most tools have a deburrer built-in. With brake cables, you want to make sure you try to cut as cleanly against the helix at a single point (try practicing different small angles). With derailleur cables, the strands run perpendicular, so you want to cut at a perpendicular angle.
The OP has clarified that s/he isn't talking about the housing but the inner cable:
If you're using a dremel tool, it's helpful to wrap some electrical or other tape around the cable before you cut. This helps prevent the strands from untangling. Work in small cuts so you don't overheat the metal and start melting the teflon coating too much. Melted teflon gas is harmful so give yourself good ventilation.