Function of datarate, and how much you can tolerate INL/DNL errors between samples. You would also need to consider the BW of the sawtooth, since you would need 3rd, 5th, 7th, Nth order harmonics content depending on the desired edge rate. So if your 1st Nyquist zone (i.e. the band between DC and the Nyquist rate, Fs/2) only covers the fundamental ("1st order" harmonic), you will get a sine wave at the output...
This applies to any DAC, not just the AD9106. See the AD9106 datasheet for more details, specifications, etc.