It will be killed by a -5c frost. When I've used it I sow it in September then it won't flower until the following year, so it should die over winter. No cutting or chopping needed, if there are still stalks etc in spring you can rake them off. Or just not bother. Unless it's that one you grow for suppressing nematodes, you might need to dig that in?
I'm pleased i didn't sow it last year as the coldest frost we had was -3c so most of it would have survived