Why does canned food expire soon once the can is opened? Canned food can maintain 1+ year in good state. However, when you open the can, the countdown starts.

I read it happens because microorganism from the outside reach the inside of the can. 

My question is: Is it possible to keep food inside the just opened can free of microorganisms? Maybe moving immediately to an airtight container and take out the needed amount with a cleaned spoon? (If a cleaned spoon still contains microorganism --- why clean it in the first place?)
No.

When you can something, the temperature and pressure kill bacteria and micro-organisms. 

Once its exposed to air, you're exposing it to bacteria and micro-organisms. Despite you thinking the spoon is clean, it still has some bacteria and micro-organisms on it which will get into the food. And your "airtight" container is likely not nearly as airtight as a can.