I've got a tire with a good amount of tread left, but there's a cut from glass that goes through. It's pretty small, a few mm. However, I've now had two leaks because stuff seems to be getting through the cut to the tube I guess. Anyone ever plugged a cut with shoe-goo? Or is there something else I can use as a permanent repair so I don't have to buy a new tire yet? Seems a shame to retire a tire that is otherwise in very good shape. Thanks....

Duct tape on the inside will work

Permanent .. nope. because of the way tires are made cured in heat and pressure ..
, you are talking temporary fixes ..

tire boots span compromised tire casings ,,

maybe get some big truck tube tire patches

mr tuffy tire liners

thorn resistant tubes

etc.

If the fabric cords in the tire casing have been cut, which sounds likely since it goes all the way through, the tire is a goner and you may as well replace it now before it fails suddenly, probably at the least convenient time.

My test is if I can feel a bump on the cut area after the tire has been inflated to full pressure.

If there's no bump, I'll stick a piece of duct tape on the inside like 10 wheels said.
If there's a bump, however small, like dsbrantjr, I assume a cord (or more) has been cut so I replace the tire while it's convenient rather than wait for it to fail on the road.

I use shoe goo in little cuts that don't go all the way through. Can't really say how effective it is.

Like dsbrantjr said, if the cords in the tire casing are cut, it's irreparable. Last year, I ran over something that cut the cords on a brand new tire. Only had about 10 miles on it. Grr...

You can "boot" the tire as a temporary fix. (How temporary? Depends on how lucky you're feeling.) A tire boot is basically something that resists stretching, applied to the inside of the tire itself, to provide structural support where the tire's cords are cut. Park Tool sells tire boots. I use scraps of kevlar fabric from drum heads (my other hobby). Tyvek mailing envelopes are reported to work well. Dollar bills work well enough in a pinch if you need to improvise a roadside repair to limp home.

Shoe-goo is good for filling in gaps in the tread... so other stuff can't get in there and make the gap bigger... it doesn't patch any leak and it won't repair damaged casing.

I've used various materials as boots to hold the tube inside the tire until I can get to a bike shop, but I wouldn't trust any of them as a permanent fix. Having a tube blow out through the tire sidewall while you're whizzing down a hill at full speed is some scary sh-t. I survived it once, but I think twice would be pushing my luck.

Oh, well.....off to get a new tire, I guess. Jeez, you'd think we can put a guy on the moon and make self-driving cars, there ought to be a self-healing tire! I know tubes can do that, why not tires?