When olive groves are cultivated on clayey soils with steep gradients, as in many Mediterranean areas, reducing the runoff and soil erosion rates by adopting proper soil management practices is imperative. A soil cover by pruning residues may represent an alternative to the commonly adopted mechanical tillage. This study evaluates the water infiltration rates and surface runoff volumes in a steep and clayey olive grove of Southern Italy. These hydrological variables are measured at the plot scale under four soil management practices (mechanical tillage, total artificial protection of soil and soil cover with two different rates of vegetal residues). The measurements have been carried out using a rainfall simulator under dry (undisturbed) and wet (that is, on soils disturbed by intense rainfall) conditions. The mechanical tillage leads to lower water infiltration rates and higher runoff production. The retention of a soil cover by vegetal residues (in the range 3.5–17.5 tons/ha of dry matter) reduces the runoff rate on average by 30%, mainly because of the increased soil infiltration rates (over 100%, compared to mechanical tillage). After soil disturbance due to antecedent rainfall, the runoff generation capacity of a soil disturbed by a heavy precipitation significantly increased compared to undisturbed soils because of the decrease in soil infiltration rates. Overall, the retention of vegetal residues over the soil may be advisable to reduce surface runoff generation rates, particularly for saturated soils.