Answer: Clematis can be grafted, yes. In this case you can try to mend it. Align the broken vine as exactly as you can (the goal is matching cambium to cambium), wrap it with electrical tape, then seal with wax. When the vine has had time to heal and begins growing normally again, remove the tape. The odds of this being successful are not all that high, but no harm in trying.
I wonder, though, if this is damage due to wind, a bunny nibbling, or if this is a case of clematis wilt. Here is some information about it.
If you do have to cut it back below the break, it should regrow relatively quickly due to the established root system. Good luck!
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