In theory, you might lose some of the strength of the carcass. You might feel nervous driving a car with a (repaired) 1″ gash in the sidewall, so it’s difficult to recommend that other people do the same with bike tyres. But FWIW, I’ve patched the inside of tyres when there’s been a hole. It’s worked just fine for the lifetime of the tyre.
I’ve tried suturing the sidewall previously (in my case with surgical sutures) but ended up tearing more holes and it would never seal. So I just use (large) inner tube patches and vulcanising glue (the stuff you get in puncture repair kits).
But you’re describing a ‘slice’ that doesn’t go all the way through and there’s no bulging / leaking. When is a slice in fact a scratch??