If I have a minim (half note) and a tempo of 96 in cut time (2/2), what does it mean? I'm doing it in 96 tempo but don't know if that's correct, or should I do it in 192bpm?
In your comments you have clarified that it is a minim not a dotted minim
What does a minim = 96 bpm mean?
This means minims would be played at 96 beats per minute. For a simple metronome with bpm relative to a crotchet you would simply need to double the bpm because a crotchet is half a minim.
Therefore, yes your tempo in respects to crotchets would be 192bpm. However, musicians do not play this speed on the metronome and instead play 96bpm but every "beat" plays the length of a minim.
Thus, the following bars have the first 2 bars equal the last 2 bars (in terms of duration):