David Ortiz sat up and walked ... his wife, Tiffany Ortiz, says -- adding that Big Papi "is making good progress towards recovery."
The Boston Red Sox legend was shot in the back on Sunday night in the Dominican Republic ... and he's undergone multiple surgeries to fix the damage that the bullet caused.
But, Ortiz's wife says he's healing up ... saying Wednesday, "Yesterday and this morning, David was able to sit up as well as take some steps."
"His condition is guarded and he will remain in the ICU for the coming days, but he is making good progress towards recovery.