It should be made clear that in the context of construction projects and bringing things back to the baseline programme, the terms Mitigation and Acceleration are different things.
Through general observations working in the industry, it seems that a lot of people confuse these terms and get themselves into commercial issues because they've inadvertently Accelerated a programme, spending money that they don't have to do so. A lot of the time it happens when people try to force the programme to fit without being able to present the benefit analysis of carrying out that Acceleration (or what they believe to be mitigation), to their own bosses, the client or key stakeholders.
So what is the difference then?
Mitigation is finding a better way of doing something or gaining an efficiency without expending any extra effort. So in a programme sense, it's resequencing to reduce or mitigate the impact of a delay whilst only utilising the existing resource available and therefore not having to spend anymore money or effort.
Example: due to current events, there is a forecast delay to a project due to late design information which will impact the subsequent manufacture of a product. This means that the current forecast programme sequence and critical path in construction will be delayed. However, it turns out that design is more advanced in another area of the project and the programme can be resequenced to be built in a different direction to mitigate the delay. This effectively switches the activities and resources on the critical path around, resequencing the problem area in design and manufacture to maintain the original durations without impacting the overall project.
Acceleration is an option that is applied to a forecast delay when it can't be solved through mitigation. Acceleration means that there will be additional effort required to complete in the same time-frame as before. Obviously, more effort over and above what was originally allowed for or intended, will carry a price to someone and therefore has to be instructed by the person who will be paying the bill, if it is considered necessary or worthwhile to do so. It's just science:

Example (Re-framed): there is a delay to design and subsequent manufacture of a product that means that the original programme sequence and critical path will be delayed. The delay can't be mitigated by resequencing as design has not progressed for other areas of the project where resequencing might have been able to take place. So to achieve the completion date, acceleration needs to be considered in order to account for the additional effort required to meet the deadline in a reduced timeframe. There could be numerous ways of offering acceleration. If design cannot be accelerated, one proposal might be to add additional resource to the manufacturing team to reduce the overall lead in for materials to maintain the planned start on site date for construction. If this is not possible, the risk might shift later to construction where increasing the number of shifts on an activity may have the desired effect.
Notice the use of the present and future tense in these examples. Potential Delay is always best dealt with as soon you become aware of it so it can be forecast and actions to prevent it agreed up front, especially when there is still the opportunity to accelerate available. It then allows decisions to be weighed up and made around programme, cost and quality before they happen. Then, a prior benefit analysis (on some level) can be carried out by which to base the decision.
There is always a duty to mitigate delay in construction contracts, but be careful about how far you can realistically go with this before it becomes apparent that really, Acceleration is the only option left. Look at the resources you have available based on your programme compared with what you will need to prevent the forecast delay and see how they marry up. If it comes to it, Acceleration is the last resort for a project in forecast delay and all stakeholders need to be made aware of it.
It's worth re-emphasising to remember the maths and physics again here:

Acceleration becomes an option to be considered as a result of some sort of change. So when looking at acceleration options, consider the earlier it can be done in the process the better because if the first option fails, you still have some time to look at implementing another option or a combination of options if time or cost still allows. The risk is lower the earlier this can be done.
So when your project slips and you're trying to bring it back to the baseline, keep in mind the differences between Mitigation and Acceleration.