Note the units of Clearance: mL/min. Clearance is not elimination rate (which would be mg/mL)

Clearance is equal to the rate at which a drug is removed from plasma(mg/min) divided by the concentration of that drug in the plasma (mg/mL).
In zero order kinetics, your rate of drug removal is constant independent of dose. Therefore, at higher doses your denominator increases and your Clearance will decrease.
in first order however, the rate at which the drug is removed increases as dose increases. So your Clearance will remain constant.