In the text
You're procrastinating. No, worse than that[punctuation] you're avoiding the problem.
a comma is probably the most likely punctuation to be used after "that". A comma is reticently an acceptable option here. A period would be most unlikely, because "No, worse than that" is not really an independent sentence, although it could be parsed as one. In my view a semicolon is undesirable for the same reason, although some people would use a semicolon here. a dash is possible, as is a colon. But if a dash is used, I would favor matching it with a dash after "no". But "No, worse than that" is a common set phrase, and so some would feel the dash to be out of place within it.