As far as I'm aware, there's no plan for rocket refueling on Mars. That makes sense, considering that the stages we normally think of as the 'rocket' will be gone long before our pods get to Mars.
We will refuel the pod, which has its own rocket engines on it, and use that to get back up (with a tiny fraction of the original payload) from the surface. Mars' gravity well and atmosphere are a fraction of Earth's, so there's really no need for a multi-stage rocket and all that. A refueled and weight reduced pod will do it just fine.
You could probably put a rocket stage capable of a Mars landing and then takeoff after refueling on top of a stage capable of an Earth landing.
I think this is being looked at, as though the gravity well is smaller than Earth's, it is not small enough for a crewed pod ascent like the moon landing.
From my understanding this is one of the reasons other than looking for life to want easy to access water, as then you can make rocket fuel with solar panels.
Mars would almost certainly require a small rocket to get to orbit, but it would be trivially sized compared to what we need on Earth. Even something as small as the Atlas rockets that brought the first Americans to space would probably be overpowered compared to Mars' small gravity well. Throw in atmospheric losses less than a hundredth of that on Earth and suddenly space becomes very accessible.
Short term and primary goal? Significantly cut down the costs of access to space. But long term goal is landing and taking off from another worlds, and this project produces important engineering insights that may prove useful for that goal. SpaceX has a habit of hitting multiple targets at once.
