This can be better explained by using physiotherapy as an example.
Say for example you are injured in a car crash that was not your fault. Another vehicle drove into the rear of your vehicle and as a result you sustained a whiplash type injury. It is likely that the other side will offer to pay for a course of physiotherapy treatment for you. If this is offered and you decline the treatment then the Defendant could (and most probably would) argue that you are failing to mitigate your losses. By having physiotherapy treatment the idea is that your injury may resolve earlier. For example with physiotherapy treatment you may make a full recovery from the injuries you sustained in the accident within 6 months. Without such physiotherapy treatment you may not recover from the injuries you sustained in the accident until 9 months after the accident.
In personal injury claims, compensation is awarded for the nature and extent (length) of your injury. If you prolong your injury by refusing to attend for physiotherapy treatment, it is likely that the Defendant will argue that you are failing to mitigate your losses. You can of course recover your reasonable expenses in attending the physiotherapy sessions (whether that be bus fares, petrol expenses etc).
So in a claim we will always advise you to mitigate your losses. We can always try and recover your expenses from the other side, but you are under a duty to keep your losses to a minimum. This extends to things like travel expenses. Say for example you take a taxi to and from the physiotherapy sessions when it was reasonable for you to take a bus, which would have been much cheaper. We can try and recover the cost of the taxi fair but the Defendant is likely to argue that you have failed to mitigate (or minimise) your losses. Therefore, there is always a risk that the taxi fare will not be recovered in full. It is all a case of reasonableness.