Both players were substituted in the Boxing Day win over Scunthorpe before the full extent of their problems was announced on Friday.
Collins has suffered a triple fracture to his cheekbone and will be out for up to two months, while Miller is likely to miss the rest of the season with cruciate ligament damage.
"Neill looks set to be sidelined for anything from four to eight weeks," manager Danny Wilson told the club's official website.
"He was operated on straight after the game on Wednesday and he won't be able to train for a while."
He added: "It is more bad news with Shaun. It looks like we have lost him for the season. He has damaged his cruciate ligaments and will be missing for around seven to nine months.
"It is especially frustrating for the two lads, who are both at the top of their games, Shaun in particular. He has been in excellent form and has worked so hard to nail down this opportunity since arriving in the summer."
United’s next match is at home to bottom club Hartlepool on Saturday.
Defender Tony McMahon will also be missing for the Blades as he serves a one-match suspension following his fifth yellow card of the season against the Iron.
Goalkeeper Mark Howard (thigh) and defender Lescinel Jean-Francois (knee) are working their way back to fitness but are unlikely to be risked against a side with just one win all year.
Hartlepool, meanwhile, have won just one game all season and none since John Hughes took the reins from Neale Cooper in November.
However, Pools were able to include Nathan Luscombe (knee), Simon Walton (hamstring), Peter Hartley (conjunctivitis), Evan Horwood (groin) and Luke James (tonsilitis) for the 3-0 defeat to Carlisle.
Midfielders Luscombe and Walton were unused substitutes while teenager James came off the bench as Hughes eased his absentees back into action.
Goalkeeper Andy Rafferty is still on the sidelines due to an operation he had on his knee over the summer.