Not without first filling the oceans and atmosphere with toxic amounts of oxygen, driving all slimy things that couldn't adapt fast enough into extinction: https://en.wikipedia.org/wiki/Great_Oxidation_Event

On the plus side, since we descend from slimy things that survived the carnage, we have fairly good oxygen tolerance and completely removing all CO₂ might not even hurt all that much.

Provided that the things that used up all the CO₂ were close enough to eat, anyway. Otherwise we'd be left without any agriculture, which would be bad.