I actually found cutting just by drilling the (continuous) stripboards rather iffy if you want to use (for leads) the holes adjacent to the one being cut out to interrupt a strip. Using a 2.5mm drill leaves the adjacent holes intact, but sometimes leaves a sliver of copper on one side when the hole is not well centered from the factory. Simply using a 3mm drill avoid this issue but makes it rather easy to ruin part of the copper of the adjacent holes on the same strip. So what I end up doing is to first scratch with a cheap cutter two lines to separate the hole I'm going to drill, and then then drill it with the 3mm drill. It turns out you hardly need a handle (let alone machine power) if do it like this because the scratch/cut marks make the copper around the target hole strip much easier and—more importantly—in a predictable manner, without stripping parts of copper surrounding the adjacent holes.
Of course, what I said above matter only if you care about the density of the stuff on your stripboard; if you're willing to design for losing/skipping 3 holes in a row, then you can be much more expedient with your drilling. The photo of the board from the instructables in the howto linked in the accepted answer looks to be of this latter kind of slack design.
And I suspect you mileage may vary based on the relative strengths of the board's material. I've only used FR2 stripboards insofar and on these when you drill the copper essentially doesn't come off the substrate but rather the substrate flakes off with bits of copper still attached, which probably explains why cutting the copper first matters in what shape it comes off. I see that there are FR4 stripboards for sale, but I personally don't see a good reason to buy a more expensive board that you're going to make mess of anyway... unlike in the case of protoboards that don't require you to make disconnects. YMMV on this aspect too, I guess.
Addendum. After wrting the above, I found a guy who even uses/saves every hole by cutting two scratches between the same pair of holes (instead of bracketing one with cuts like I do) and then he uses a knife to slide underneath and lift the bit of copper in between the cuts. On my first attempt to replicate this technique it took me four tries to make the bit in between the cuts to peel off. So it seems to me less straightforward than drilling that in-between chunk out, but with a bit of practice it's probably reasonably easy to become proficient at this knife-only technique. Perhaps using an appropriately sized chisel might make this scooping technique even faster.
Later edit: Well, after purchasing a higher-quality board of this stripped type (UL 94V-0 certified, cost approximately 4 times as the el cheapo stuff), much of what I wrote above turns to be a poor-man's tradeoff of time for money. On a quality board the holes are all well-centered and the substrate doesn't flake so a quick touch with 2.5mm drill mounted on a ~300rpm electric screwdriver works as expected and takes only a fraction of the time.