Seem to have torn a small part of the underside of my tongue.

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The little red part in front of my teeth

It's not the frenulum, just to be clear. It should heal fine, probably, right? Should I cut the dangly part off?

>>16797795
Looks like something called plica fimbriata. Residual tissue that just kind of hangs around instead of falling off/reabsorbing like normal.
Not normally vascular, so bleeding shouldn't be too bad if you do decide to cut it off.
***BUT if you choose to cut it off, you really need to sterilize whatever tool you use to do it. Infections are a bitch. Not fun.

>>16797819
So I have no choice but to cut it if I want it gone? Fun.

>>16797849
I had one on each side of my frenulum. Cut both off. Stings pretty sharply for a split second, but then it's over. Oral mucosa heals super quick so it'll be completely healed in something like 2 days.
Pro-tip: use a clamping tool to remove it (clippers, small scissors, etc.) as opposed to an open blade (knife). You can get it in position, then make the cut pretty quickly that way. Won't hurt as bad.