My wife and I have been licensed and active EMT's for the last 20 years. Over the last few, we developed a couple of presentations about the first 3 things to do in a medical emergency onboard (not a cut but something serious like a finger being lost as above, a cardiac event, a stroke, anaphylactic shock, etc). We've given it to about 2,000 boaters so far and are doing a couple more presentations of it over the next few months - at the SSCA GAM in Annapolis at the end of September and River Dunes Marina in Oriental, NC the first weekend in November. These are basic skills that everyone should know when you're on a boat.
I'm glad to see the situation done above was a MAYDAY. You're way more apt to issue a MAYDAY for a medical emergency than for a boat taking on water and yet most people make the call very late.