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GiNaC, the C++ library used as the backend for symbolic expressions in Sage, supports Clifford algebras. See this article for more details. Using this implementation might be easier than starting from scratch in Python/Cython. I expect the performance of GiNaC to be quite competitive, thanks to Pynac we can also use arbitrary coefficient domains from Sage.

After a brief look at the article mentioned above, I can say that it would be fairly straightforward to wrap those C++ functions and provide access to these data structures from Sage. I would be happy to do this and create a prototype implementation if somebody is willing to take over the polish. :)