Disclaimer: I'm not a mini-expert. In fact, this was the first time that I've assembled mini's. Usually the ones that I buy are fully assembled. I've built plenty of snap together and glue models as a kid, but this was new to me.
It took me about 3 hours to assemble all the mini's. I used snips, a razor blade, glue, and bandaids.
TECHNIQUE #1 The first technique that I tried was to use the snips and cut the sprue as close to the figure as possible. Even with snips that had a flat side, there was usually about 1-2 mm of sprue left on the figure. This I'd carefully remove with the razor blade, shaving it down a little at a time. This technique worked, but was slow and bloody (literally). In some cases I shaved a little too much, but not so much that it is a problem. I just say that marine has a ding in his armor from a previous battle.
TECHNIQUE #2 After I grew weary of the time that technique #1 took, I started to punch out the next set of figures. I held the sprue with one hand and pressed down on the figure, usually in the figure's center of mass. To be fair, I only tried this on the marines, as they tended to be more compact; I'd worry that genestealer arms, for example, would get bent or left behind. In most cases this was quick and resulted in very little to no sprue left on the figure. Sometimes I had to push quite hard to get the figure to pop out, and I was worried that I might end up breaking the figure. I refused to use this technique on some figures since I was afraid that a delicate feature would be left on the sprue. I stopped this technique because my pushing fingers were getting sore.
TECHNIQUE #3 (the one that I recommend) Ultimately I tried a hybrid technique. I used the snips to cut the figure off the sprue, leaving a good chunk of the sprue still on the figure (maybe 5-7mm). Now, with the figure off the sprue I had easy access to each sprue stub, which I twisted off. In all instances the twist off broke cleanly at the figure, with virtually no sprue left on the figure. There were one or two sprues that were attached to delicate features that I still snipped/shaved off rather than twist, but that was the exception.
The only thing that I broke during cut-out was a delicate chain hanging off the waist of one of the marines. I had other issues with the length of the pegs and tightness of fit that resulted in 3 broken arm pegs, but that's another story.