Are you meaning autumn raspberries? They are cut down to the ground after fruiting, with the normal summer fruiting type there is the next years' growth coming up while they are fruiting, so you would lose that. Then there are supports and wire to remove?
I think it would be easier to just cut them down and throw them over to the goats.
Come to think of it, maybe not a good idea, dried rasperry leaves are given to goats to help with kidding, something I read somewhere discouraged me from feeding to much raspberry foliage, can't remember but I'll try and find it later.
Mine don't like it anyway :-)