Spider mites aren't insects, so many (all?) insecticides won't work on them. However they don't like water, so put it in the sink or shower and spray it on all leaf sides. You may need to repeat this more than once as new mites hatch. I wouldn't use a systemic regardless, both because it is indoors along with you and any visitors, pets, family, etc. while many pesticides are intended for outdoor use, and also because any bees that come to the flowers once it is outdoors will be poisoned by the insecticide. As soon as days are above freezing, start putting it out in shade to begin hardening it off, but bring it in at night when it is colder since it is still getting too cold for a fully leafed out clematis at this point in 5a New England.

Thanks very much, NHBabs. I gave it a comprehensive spray shower an hour ago, and I also washed the stick and soil. I also sprayed down a rescued shishito pepper plant (its leaves look junky as well).

I strongly prefer not to use any 'cides on my plants or in my gardens. I did not yet lop off the top growth. Think I'd be wise to do that?

I probably wouldn't right now, but maybe when you plant it out if it's still spring.