Mars is unlikely to be a pit stop in the near future, because of the deep gravity well.

Its moons could be though, espccially Deimos as it is a type of asteroid that may contain volatiles such as water ice. It could even be used to supply water to LEO,

The Deimos Water Company

Though now we know that there are probably volatiles at the lunar poles, then our Moon is a more likely "pit stop".

Still, in  a future with rapid space transport, you could imagine stopping off at Deimos.

Any spaceship that goes through the asteroid belt would also go past the asteroids. But - if you go from Earth and boost out past Mars, say to Jupiter, then you will be going pretty fast when you pass Mars and also when you pass the asteroids. Stopping to take on fuel or water would be as much a handicap as an asset.

More likely would be some other system.

So, let's think about how it could work?

WAYS TO USE A MOON OR ASTEROID AS A PITSTOP AS YOU FLY PAST IN A SPACESHIP

Perhaps the supply station on the asteroid or moon would launch specialized supply rockets that would rendezvous with you as you go zipping past, using a lot of the fuel they contain to match velocity with you, transfer fuel then the now much lighter supply rocket returns to its base.

A spinning asteroid could have a tether attached to it, which could be used for very efficient boosting to high speeds. Basically turn a small amount of the spinning angular momentum of the asteroid into delta v to intercept the passing spaceship.

Then as before deliver fuel, and now the supply vessel is much lighter so easier for it to return to base using whatever is left of the volatiles.

I've not seen this suggested before, but it sounds like it could work.

USING ASTEROIDS AND MOONS FOR "FLYBY" TYPE BOOSTS, EVEN THOUGH THEY ARE FAR TOO SMALL FOR THEIR GRAVITY TO MAKE A DIFFERENCE

Incidentally someone proposed a neat way a spaceship could use an asteroid for a course correction. As it goes by, it fires a flexible tether with a grappling hook attached. This catches on the asteroid, and then the tug on the tether causes the spaceship to change direction, Then the spaceship releases the grapple and reels in what is left of the tether ready to repeat the process next time it passes an asteroid. That way you could do zig-zagging paths through the asteroids, or use them for flyby accelerations and decelerations using the orbital motion of the asteroid, much like you do for flybys of planets.  I can't remember where I saw the paper, but it's a fun idea :).