to cut someone loose
means to "free someone who is being bound" (as in a rescue operation) and may even imply that the person being freed is then motivated to escape or run away
The prisoners were cut loose from their chains.
In the sentence
The children were cut loose from their class.
the children where freed from the shackles of establishment imposed education and ran to the ice cream shop
the action would be understandable, however, for classes, better phrasing might be
The children were let go from their class.
since there probably wasn't a rescue operation which freed the children.