If the bark on the damaged area hasn't turn black, just cut back to live wood or leave as is if the rabbits have taken it back that far. You can always remove it later in the year after it's produced a bloom. Sometimes a wound will heal itself. You can also remove it to the ground but I'd wait until I saw new growth coming from the ground. The buried portion of the cane should send out new growth from buried buds.
Protect what's remaining with circles of chicken wire.
Rabbits seem to pick on a few bushes eating sweet tender new growth as it appears.

Thanks again Karl.