Can turkeys run around when their head is cut off like chickens do?
The brain does not control all bodily movements. Some movements are to a great extent controlled by neural networks in the spinal cord. The spine contains a network which is pre-programmed to control the muscles in frequently-used movements such as running or swimming in chickens. This is why a chicken can run away after you chop its head off. Likewise, turtles swim using their a spinal neural network. As long as a signal is received somewhere in this network, the network will activate the swimming movements. Such a system is coined an ‘attractor network’ (source: Science Nordic). A similar system has been shown to occur in a sea slug. I couldn't find similar information in the turkey though. Happy Thanksgiving :)

Note that walking and running in higher animals (mammals) is controlled by the motor cortex higher up in the brain, involving a more complex system including the pyramidal system. Reflexes, however are controlled by quick, short spinal relay circuits in higher animals as well.