Little Joe is dragged by his horse, presumably because his foot is stuck in the stirrup. Once the horse comes to a stop, we clearly see that his ankle is hitched to the saddle with a strap and snap. When the angle changes, we see that Joe takes his foot loose from the stirrup (no strap).
In the beginning, when Little Joe is speaking to the prison warden, we see over the warden's right shoulder a man hammering, and we hear his hammer striking metal. It is quite evident that he is not actually hammering anything because his arm comes to a stop before his hammer hits the spike.