The 52-year-old has left his role as assistant manager at Kilmarnock.
Nicky Devlin, Jack Fitzwater and Stephane Omeonga are among those confirmed to be leaving.
The first time the two sides had met in the final of the competition was also the first time the showpiece finale was hosted at the national stadium.
The club could be relegated from the cinch Premiership on Sunday.
A point will be enough for Killie to finish 10th and escape a play-off final against in-form Partick Thistle.
United must win at Fir Park and hope Kilmarnock beat Ross County while achieving an eight-goal swing against the Staggies.
Livingston have won only four of their last 17 games in all competitions.
County need to beat Killie to avoid a relegation play-off.
The Dons sealed third place in the cinch Premiership on Wednesday night.
A fourth loss on the bounce on Wednesday all but consigned them to automatic relegation.
Reports claim the 35-year-old has decided to call time on his career.
Killie need a result against Ross County to avoid a relegation play-off.
Butcher went off with a foot injury during Wednesday’s 1-1 draw at the Tony Macaroni Arena.
The Staggies have collected seven points from their last four games.
The 36-year-old replaced Robbie Neilson on an interim basis last month.
The Edinburgh rivals are battling for fourth spot in the cinch Premiership.
The Paisley side made the top six and will sign off their campaign against Rangers on Saturday.
The English defender has decided not to renew his contract with the Lions.
The Jambos are two points ahead of their city rivals going into the last games of the season.
Jim Goodwin’s side are three points adrift with one game left of the cinch Premiership season.