Answer: Your clematis should regrow just fine from the roots and buds on the remaining stubs. The only potential problem I can think of is the plant was grafted and the rabbit ate it off below the graft. You may also find, depending on the type of clematis you have, that it does not bloom until the following year when it has developed "old wood" again. You might want to protect the vine from now on so the rabbit does not eat any more.
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