Can bone get infected if you have deep hand cut?

Yes: Bone can be infected with deep cuts.The wound should be cleaned with running water and soap and check signs of infections.

Yes: Usually only after uncontrolled soft tissue infection.

Open fracture: With a deep cut that exposed bone can get infected if the wound get infected, it is not a typical scenario. However if the cut also cuts the bone such as with a saw, or there is devitalized tissue or there is an open fracture risk goes up. If the cut is due to a dirty source such as a bite or a farm injury and there is bone injury then that must be washed out properly to avoid severe bone infect.