The fundamental basis of the employment contract is that someone agrees to devote their time and attention to carrying out work for you during the agreed time and you pay them for the hours they spend working.
As part of the implied term of faith and fidelity an employee is supposed to devote the whole of his attention during work time to his employer’s interests. This is not consistent with running his own business during the time he is working for you.
He may also be in breach of specific terms depending on what your contract says about carrying out other work with or without express permission. If he is not carrying out the work you have assigned to him during his work time then this is misconduct and, depending on your contractual terms, it could potentially be gross misconduct.
Consider your handbook and see if you categorise this behaviour in a list of behaviour that is considered misconduct or gross misconduct. Most companies, where they give examples of misconduct, include “the failure to devote the whole of your time, attention and abilities to our business and its affairs during your normal working hours”.
However, some companies will list under potential gross misconduct “undertaking private work on the premises and/or in working hours without express permission”. Once you have identified what terms you have in place then you can be clear on the severity of the issue.
This is potentially serious misconduct even if not gross misconduct. Do you have a policy on using personal phones during work time? The amount of time he spends doing this will help to determine the severity of the situation. Putting him through the disciplinary process should help discourage this behaviour and improve performance. If not then dismissal is very much on the cards.