I am aware of no University that automatically does anything. That said, most Universities, have policies in place to protect their reputation. At Cambridge, both Christ's College and Griton College have almost identical policies which makes me think there is an underlying university policy that I cannot easily find. To quote Griton's policy:
Additionally, the University has a number of sanctions for behaviour impinging on the image of the University, while the most serious breaches, including all criminal behaviour, will be referred to the local police.
Basically, Universities should be reporting any criminal activity to the local authorities. They also have the right to follow their own policies, of which expulsion is a possibility. Universities like to protect their images (e.g., the recent sex offence scandals in the US). So what the University will do may depend on if the victim of the crime was another student and how vocal the sides are.