A failed worm wear or damaged planetary gear assembly can prevent the beater from spinning. If the beater doesn't move at all when the motor spins, then the worm gear is likely stripped. Unplug the mixer, examine the worm gear and replace the gear if it's stripped.
If the beater moves around the inside of the mixing bowl but the beater itself doesn't spin, then the pinion gear inside the planetary gear assembly is likely stripped or damaged. Unplug the mixer, pull off the planetary gear assembly and replace the assembly if the pinion gear is damaged or stripped.
These repairs may help solve your stand mixer problem
Replace the stand mixer worm gear
The worm gear driven by the vertical shaft and pinion gear rotates the attachment. If the attachment will not rotate, replace the worm gear.
The planetary gear spins the beater as the planetary housing moves the beater in a circular motion to orbit the inside of the mixing bowl. If the beater moves in a circular orbit around the inside of the bowl but the beater doesn't spin then the beater gear inside the planetary housing is likely stripped or damaged. Replace the planetary gear assembly if the beater doesn't spin when orbiting the inside of the mixing bowl.