I'm not that experienced with DAC audio applications, but there is a relationship between the highest audio frequency you wish to process and how fast you have to send the data to the chip. Something about Nyquist theory that the sample rate has to be at least twice the speed of the highest frequency to be produced or reproduced.
I'm sure there is more experienced people around here to help you, but the first fact to be verified is can the Arduino will move data fast enough to the DAC to be able to reproduce the audio frequency range you wish to process?
Lefty