If a guy wants to marry a girl who is staying away from her husband for 6 months but hasn't taken a khula yet, what is the ruling in this regard ? Can they do a mutah?

He cannot marry her unless the divorce is issued and she waits 3 cycles for the waiting period. Even if she is away from her husband for 6 months now, she is still his wife according to Islamic Law. The divorce must be issued in order for her to separate from her husband and remarry after the waiting period.