Classic for many puppies, but I'd suggest ESPECIALLY for the Border Collie puppy. Now is the time to teach your new puppy that biting and jumping up on humans is NOT to be tolerated. Before he becomes an out of control youngster. When he gets this excited, end the contact. Stand up, say NO BITING, take him outside to empty and back to his bed. Preferably too, a crate. Better would be not to let him get that worked up but good luck with that, in a BC. This is a breed that is best when given a job to do - and all too often they end up in Rescue because people don't realise this breed needs constant exercise and mental stimulation.
Now is the time to set the ground rules, not overly harsh, but with clear correction so he moves into adulthood as a happy bidable dog.
ps He will chew when teething, but if he's under 4 months, this is mouthing which he'd have done with his siblings who would have yelped and TURNED AWAY, ending the contact. It's the turning away that you should copy.