Learn Swedish: Jag andas med magen. - I breathe with my stomach.

No, andas is a deponent verb. This means it looks passive because it ends in -s, but it actually has an active meaning ("to breathe"). You have probably seen other verbs like this already, such as hoppas (to hope) or minns (to remember).

Since andas is a deponent verb, how do I use it in the past tense?

It conjugates like this: andas (present), andades (past), and andats (supine/"have breathed"). So, "I breathed" would be Jag andades.

Why is it magen (the stomach) instead of min mage (my stomach)?

In Swedish, it is standard to use the definite form (like magen) for body parts and clothing when it is obvious who they belong to. Since it is your own body doing the breathing, you do not need to say min.

In English we often say "breathe from the stomach". Can I say Jag andas från magen?

You will be understood, but med (with) is the natural preposition to use here in Swedish. Swedish treats the stomach as the "tool" you are using to breathe, rather than the starting location of the breath.