Breathing removes CO2 generally. But when you are breathing normally, i.e. letting the autonomic nervous system control the breathing rate at tidal volume (the amount of air exchanged in a normal breath), the rate of purging CO2 is equal to the rate it is produced by cellular respiration so you have a normal physiological amount of CO2 in circulation.

If you intentionally breath deeply, greater than tidal volume, it means at the same breathing rate, you are exchanging more air in total and will be purging more CO2 than you produce which will lead to hypocapnia over time.

Hypocapnia doesn't inherently need to result from deep breathing if you offset the greater-than-tidal volume with less-than-normal breath rate — if you are breathing very slow or 'skip' breathing with pauses in between, but that balance can be pretty hard to reach