The MPC Key 61 does indeed have a transpose function!
Press the Oct - / Oct + buttons to transpose the keyboard down or up one octave at a time. The lights below this button will indicate the current octave setting. Press and hold Shift and press the Oct - / Oct +buttons to transpose the keyboard down or up one semitone at a time. Press and hold both buttons and press a key on the keybed to set the transposition to that value. Press and hold both buttons and release to reset the transposition.