I have an LED strip that uses around 2A from 12V DC (25W). I will probably use less than the full strip, so if I cut the strip, will it draw more current (the voltage will stay at 12V) or less? I want to figure out if the LED's will get brighter or hotter if I use less of the strip.
Another way you could look at this situation is that removing a few LEDs will not influence the voltage over the other LEDs(all in parallel), so the current through the remaining LEDs will stay the same while the removed LEDs do not draw current anymore of course, so the required current is less.
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.