Dunno about Italian grindcore, i mean i probably have some on some compilation tapes somewhere, but nothing really that rings any bells.
Italy had a real good hardcore punk scene during the early 80's however, with bands such as Impact, Blue Vomit, Rappresaglia, Negazione and all those side-projects by the Cripple Bastards members (can't name any from the top of my head but, from around 1984 to 1988)
And of course many many more...
Brazilian grind from the early days: Brigado Dó Odio (the 12" split with Olho Selco is a must have if you are into the grindstuff that predates anything Napalm Death did =P) and SP Kaos. (1985 and before, i think SP Kaos recorded in 1984 but not sure, info about these bands are not really that easy to come by)
There is an excellent compilation named "Brasil Punkcore: Could be better but also worse" covers stuff from 1980 to 1989 maybe, only obscure and underground veterans that play any form of Punk (grindcore, hardcore, fastcore. punkrock, crossover etc.).
In more recent years (90's and forward): Necrose (brutal grindcore without any fancy tricks, just brutal and in your face, you can never go wrong with their 200+ song discography tape)
And ROT! the Kings of underground brasilian grindcore! (They do suck most of the time however but the ROT/Intestinal Disease LP Split is a real ripper)
Fuck i will find that italian hardcore comp, i am sure i have at least one of these, featuring early 80's bands.
Most countries around the world have compilations like these, released by people who where in the scene at the time.
End of rant and not really Metal related at all, but proto-grind related i guess? ^^
I will leave you to it with this Spazz wisdom: Fastcore has always been around, in every country it can be found.
You could also check out the Italian extremepunk label F.O.A.D. Records, they have re-released many classics from the early days, as well as rare obscure ones no one have ever heard of.
Edit: Been digging in my archives and it turns out i had more Italian grind than i first thought.
Bestial Vomit https://www.discogs.com/artist/4882798-Bestial-Vomit-3
(There is another more recent grind band from italy also called Bestial Vomit, they might be the same band, i don't know. This one is from the late 80's)
Ass Ache https://www.discogs.com/artist/4763590-Ass-Ache
Nuclear Grinder https://www.discogs.com/artist/954340-Nuclear-Grinder
Grimcorpses, Harsh Feelings, Streptogrinder (The Cripple Bastards stuff, 85-94)
This is the compilation i mentioned earlier: Attitudine Mentale Positiva (1990) https://www.discogs.com/Various-Attitudine-Mentale-Positiva/release/2978498
Mostly hardcore bands, but still pretty cool.
Some other compilations featuring more Italian grind.
Screams From Italy https://www.discogs.com/Various-Screams-From-Italy/release/4763720
Pasta Power Violence https://www.discogs.com/Various-Pasta-Power-Violence/master/200447
Speed Kills... A.K.A. Pasta Power Violence II https://www.discogs.com/Various-Speed-Kills-AKA-Pasta-Power-Violence-II/release/1542297
Sposa In Alto Mare is another more recent band, they play rock n roll in true grindcore fashion!https://www.discogs.com/artist/1905856-Sposa-In-Alto-Mare