Just my 2 cents
1. If a player literally refuse to run, or say walking around in protest and scoring own goal in such a blatant way there are ways to punish him or even terminate his contract, or even extreme cases where a player is involved in criminal conduct (Adrian Mutu).
2. However bad performances, outright lazy and not giving a feck is very hard to prove. It's gonna be a long battle in arbitration court if push comes to the shoves which nobody would want. Is he bad? Out of form? Down tool? Or simply taking the piss to spite the club?
3. Clubs can't force a player out legally but have means at their disposal to "push them out" just like what we did to Bastian Schweinsteiger, making it very uncomfortable for him that he agreed to move on. Just like what we're doing with Rashford. It's not pretty but it happened more often than not. Players normally took the hint and simply move on, unless you're Winston Bogarde. Paying off one's contract simply means the club pays his salary for the full duration of the contract but letting the player leave. Club does this for cheap academy player on contract that has little value.
4. Players on the other hand have to honor their contract but have their own means to break their contract either legally (asking for a transfer and missing out on the transfer cut) or simply refusing to play until being sold. We had this instance with Ronaldo wanting to go to Madrid. Most of the times players would just tell their agents that they want to move and if the price is right club will simply sell.
5. Regarding salary cut. Technically the club can offer a new contract which is much less, but unless the players signs it club can't simply deduct pay. We have fines, disciplinary wage cut, but it's mostly 1-2 weeks salary for blatan infraction (missing a training) but hardly implementable on bad performance, unless it's stipulated in the contract. For example 25% cut if certain target are not met by the end of the season, but again clubs can't simply deduct pay based on subjective reasons such as not playing well enough
If Rashford is on 10k per week we can simply say "Here's 2.5M of your salary paid in full, dont bother to come on monday", but being on 300K per week that wont be a smart thing to do. Hence the clubs simply made the situation so untenable for Rashford that he have no other choice than to agree to move, even if it's not his prefered destination.
So yes, the club clearly push him out (rightly so). The how is just formality