Carbon dioxide clearance is not determined by minute ventilation alone. It is determined by alveolar ventilation.
That distinction is critical.
Minute ventilation is the total amount of gas moved in and out of the respiratory system each minute. Alveolar ventilation is the portion of that ventilation that actually participates in gas exchange.
Dead space is ventilation that does not eliminate carbon dioxide. Some dead space is normal.
The conducting airways move gas but do not exchange oxygen or carbon dioxide. This is anatomic dead space.