What hardware are you using to play the audio file? The Arduino doesn't know squat about audio files.
Proper hardware would read enough data from a file, so that you could also write to a different file, with only minimal chances of both the Arduino and the other hardware needing to read from and write to the SD card at the same time. Mostly the Arduino would write to, and the other hardware read from, buffers. Writing to the card, or reading from the card, happens only when the buffer becomes full (a write happens) or empty (a read happens).