Not remembering to check if I'd mined out an area before pulling the deconstruction lever, and punching a hole right through my (very crowded) dining room, all the way to the bottom. The magma forges were somewhere below that, and further down still, the housing complex.
In short: One lever killed a bunch of partying dwarves (including my miners), destroyed two artifacts, then freed magma into the rest of the fort, which destroyed four more artifacts, killed around forty dwarves without access to picks. I think it also dismantled my control room, so the siege that came immediately after mopped up any survivors, who were either on fire, tantruming, or tantruming while on fire.The food stockpile also caught fire, and magma sealed off my cistern. This was back before I fully understood the interface, so no movies, and I deleted the fortress with an earlier version.
I still make this mistake, but much less horrifyingly since I now sandwich workshops and magma under solid layers of earth. Only a few casualties from the punches, which I now use on very large scales to reduce the amount of channeling (Or ramp removal) work I have to do.
For your problem, pumps hooked into waterwheels could reduce the flow enough that you could build over the spot (just keep removing the suspend order and a mason will eventually finish). If you don't have time for that,if you have an area (for exploratory mining, say) near the area, you can seal it up and then channel the water into THAT before the place where you're leaking, reducing the amount of water that's directly threatening your fort and forcing it to take a longer path to threaten you. You can deal with it later.
If you can place hatch covers over the breach, it will stop water from passing.
And if you don't mind being a little cheesy, you can put fortifications into the edge of the map near the inflow point and divert as much water as you can, buying you time.