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.
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.