LED strip and current
If the strip is meant to be cut then all the LEDs are connected in parallel, and each of them should have its limiting resistor.

If this is true you can power the shorter strip with a 12V source, but the strip will draw less current.

Let me explain this with an example. Let's say the strip consists of 10 LEDs, each of them drawing around 2A/10 = 200mA of current. If you cut away some four LEDs the expected total draw is about 1.2A then.