Did Groot's arm grow back in a minute?

Yes, he can.

As we have seen, Groot extends his arm to make a handle for the stormbreaker. So, it is obvious that he can also regrow his arm.

We have also seen that Groot turns into an enormous wooden box to save his friends and grows more to take on firing at prison.

From Screenrant,

In 2013's Guardians of the Galaxy #3, Groot rises from a potted seedling to gigantic proportions in a matter of seconds to free the team from the Spartex Royal Guard, showing that he can grow at a moments notice. He similarly turbo-boosted his cellular growth during an attack on the Babel Spire in Annihilation: Conquest #5. Or how about that time Hulk threw a tiny Groot at Thanos, only for him to balloon in size and lay the smack down. Conversely, on several occasions, he has shown the ability to just as easily and quickly shrink down to a pint-sized sapling. So anyone whose sad over the idea that one day, Baby Groot will have to grow up need not worry, this tree comes in all shapes and sizes every day of the week.

The part how fast Adult Groot or Teen Groot can grow the amputated parts is unknown.

From the same source,

Groot is always putting himself at the forefront of danger. When he first joined up with the Guardians, he got himself killed not once, but twice on kamikaze missions. Since then, he's been burned, shot, impaled, severed in two, eaten alive, blown up, decapitated, and fallen victim to pretty much every other horrific act you can imagine befalling a giant talking tree. Given all that, it's safe to say he has endured some nasty wounds over the years. Luckily, he has a healing factor that is enough to make even Wolverine jealous.