After a year in charge, Amorim has overseen the departures of Marcus Rashford, Alejandro Garnacho and Andre Onana.
Bruce told talkSPORT: "He’s had a great few weeks, they’ve won five out of the last seven. So there’s certainly been an upturn in their performances.
"I do believe the two players in particular who they’ve bought, (Bryan) Mbeumo and (Matheus) Cunha, they’ve absolutely hit the ground running.
"They’ve shown what they’re all about and they’ve given that real cutting edge at the top end of the pitch, which maybe for a while wasn’t there.
"I have to say, he’s made a big call in the dressing room to get rid of big players, with big reputations.
"It reminds me a little bit of Arsenal, what Arteta did a few years ago where he cleared out the dressing room where people are looking from afar thinking ‘wow, that’s a big call’. So he’s made some big managerial calls."
He continued: "I think all of us (United fans) like him. We all want him to do well because underneath it all is a decent man, who’s a very, very good coach.
"And all of this ‘is he going to change his tactics and is he going to do this and is he going to do that?’ Obviously not and he stuck by him.
"Then of course, I think the big thing was Sir Jim Ratcliffe coming out last week, all of a sudden saying if the guy needs time, whatever it takes, three years."