Instead of my choice which was to advance my c-pawn to c6 (to avoid stalemate) the analysing computer on chess.com said that it I did a blunder and should have taken blacks last pawn instead. Here is the analysis output:

(-Mat15) BLUNDER - Bad news! Things were even and then suddenly you're faced with checkmate. You could have kept it even with 56. bxa3

You have mate coming in two moves, and it's White to move as it says on the diagram? The computer says to take a stale-mate? Are these the facts, or is it Black to move next on the diagram?

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I just moved to c6 to prevent stale mate. The computer told me I should have taken the black pawn. Now black will queen, but after me checkmating black by queening first.

So in the diagram it's Black's move?

c6 does lose

I suspect your blunder came on the previous moves - to allow your opponent the chance of a stalemate - and no, you don't promote your pawn with mate, because your oppo promotes with check and you lose

The best White has is a stalemate since if you don't take the pawn he'll queen it and you'll lose. Somewhere in that game you should've let the g-pawn go so you could queen one of those queenside pawns. Now Black can't lose.

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Right.

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He went for a2, which was a mistake, instead of taking my pawn and promoting and checking at the same time.

c6 is a blunder because axb2 wins for black.

Simple, really. What the computer is telling you (correctly) is that the best move for you is bxa3 with a draw. Everything else loses.

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You are right. The best thing is  a draw here for white, so the computer IS correct :-)