The issue here is the frame of reference, which is a rotating frame of reference in the case of the blades on a turbine, complicating matters since the relative speed is zero at the center and maximum at the outer edges of the blades. Like any wing or sail, the blades divert a relative flow. As mentioned previously in this thread, the change in the relative flow due to diversion can be separated into two components, the perpendicular change is related to lift, and the decrease in the component in the direction of flow is related to drag.
The relative airflow approaches a direction perpendicular to the horizontal axis of a windmill at the outer edges of the rotor blades (for a large turbine, close to 320 kph with perhaps less than 50 kph wind). Only part of the lift generates the torque that drives the windmill, while much of the drag reduces the torque, so a high lift to drag ratio is needed. Switching to a ground frame of reference, the rest of the lift and drag push downwind (relative to the ground) against the windmill. The aerodyanmic torque and force are part of a Newton third law pair, so from a ground perspective, the air exerts a torque on the windmill, and the windmill exerts an equal in magnitude but opposing torque on the air. The air exerts a downwind force on the windmill, and the windmill exerts an equal in magnitude but opposing upwind force on the air. The wind ends up being rotated and slowed down.