Some categories of melacha are permitted on chol hamoed. Are there any categories of melacha that are prohibited on chol hamoed at the biblical level (d'oraissa)?
That depends on how we Pasken.
It seems from the Gemera in Chagiga 18a that it's a Biblical prohibition to do [certain] work on Chol HaMo'ed. The Gamara brings about half a dozen verses to prove that.
But Rashi and Tosafot already argue as to whether it's really Biblical or Rabbinic [with a Asmachta (hint) on the Torah].