The cost of launching from earth is much higher than from space because we have to break Earth's gravity and pass through the atmosphere.
While this is certainly true, I don't think your general conclusions follow from this fact.
Build the next space station already. Build it big and ship it people and supplies and do it there.
The biggest expense is getting things into orbit, as you point out. It requires a certain amount of fuel for every pound or kilo of stuff we want to lift up there.
Given that space isn't exactly filled with random supplies (food, fuel for other missions, etc.) floating around, most of it is still going to have to come from Earth. So, exactly HOW is it cheaper to launch a mission from space if we still need to lift all the supplies from Earth anyway? Eventually, if we start being able to ferry people between a space station, the moon, other places, etc., we wouldn't have to lift the PEOPLE up again (if they're willing to basically live in space), but it's going to take quite a while until we can actually have a mechanism for deriving most of the other necessary SUPPLIES for missions from space... which will just have to be lifted up off the ground from Earth anyway.
So, what you're proposing is rather than flying ONE "high cost" mission up through the Earth's atmosphere, we should spend years or decades launching dozens (hundreds?) of times that material up through the atmosphere to build a giant space station or moonbase or whatever. And meanwhile, we have to keep sending up supplies continuously for any people there.
How exactly is that supposed to save costs??... except perhaps in a REALLY long term, assuming that space travel becomes an established thing in the next few decades (which is far from determined... maybe it'll catch on a few decades, maybe in a century or more).
If we cat accomplish that, we don belong in space.
From my perspective, this whole "Mission to Mars" idea is mostly a kind of propaganda move, though not in a negative sense. As other posters have said, why else bother sending humans? Robots can do just fine. But, just like the moon missions in the 1960s and 70s, this is supposed to reignite the public interest in space travel, which will make it easier to raise the kind of funds necessary to build your space station or whatever.
The first missions will be sort of "proof of concept." You're proposing investing in a giant infrastruction that will likely cost hundreds or even thousands of times the cost of one mission just to save some phantom money on not having to lift things out of Earth's gravity to launch a mission to Mars (when we had to lift most of that from Earth anyway to the space station or whatever).
I'm not saying your idea is bad in the (VERY) long term. But right now the psychological effect of launching one slightly more expensive mission that achieves a bigger goal may provide a spark. And that spark may get more people interested in the much larger amount of funding necessary to create the incredibly expensive infrastructure which you argue should make things cheaper.