I got same gun as you, 870 supermag express.
Sometimes when I do not push the shell far enough, it comes out, but that is likely a different issue.
I think the problem might be with timing of carrier or with elevator itself. It seems that when you try chamber the shell, carrier is already lifted, but the shell has not come out of magazine yet, so when shell comes out it is thrown on the ground. Look at carrier carefully (turn shotgun upside down) when you try to cycle last shell in.
Does the shell come out with force? If so, then it means that magazine spring probably works fine, and it might be a problem with trigger assembly (carrier is its part).
Is it a new gun or was it used before?
Please post your solution to the issue when you figure it out.