Main-sequence turnoff (MSTO) stars are good tracers of Galactic populations since their ages can be reliably estimated from atmospheric parameters. Based on the GALAH survey, we use the Yale rotation evolution code to determine the ages of 2926 MSTO stars with a mean age uncertainty of ~10% considering the variation of C and O abundances. The ages of CO-poor stars are systematically affected by ~10% due to the C and O abundances, globally shifting to ~0.5Gyr older compared to the results using solar metal mixture. Of the stars with [Fe/H]~0.3-0.5 or [O/Fe]<=-0.25, many have fractional age differences of >=20%, and even reach up to 36%. The age-metallicity relation appears to possibly indicate the existence of two distinct sequences: a young sequence of stars with ages mostly <7Gyr, and a relatively older sequence of stars with ages mostly >7Gyr, overlapping at 5Gyr<=age<=7Gyr. Moreover, the trends of abundances-to-age ratios show two corresponding sequences, especially in the [O/Fe]-age plane. We also find that [Y/Mg] is a good chemical clock in disk populations. The young sequence and the old sequence cannot be separated based on chemistry or kinematics; therefore, stellar age is an important parameter to distinguish these two sequences in our sample.