You can, and there are a lot of secondhand gimbals salvaged from wrecked drones sold at various prices. The repair itself is pretty complicated, but there is a guide on iFixit that would guide you through the steps.
However, even if you have a perfectly functional gimbal, you still need the carnation software to calibrate the new gimbal so it can work properly, which only DJI have access to.
The only solution for a broken gimbal is to send it back to DJI for repairs, which is exactly what they want, since they can make more money that way.