We calculate the g factor of the 6s6p (3) P-0 state of 199 and 201 mercury isotopes using a relativistic high-precision all-order method that combines the configuration interaction and the coupled-cluster approaches. Our values g(Hg-199) = -0.9485(49) x 10(-3) and g(Hg-201) = 0.3504(18) x 10(-3) are in agreement with the experimental measurements within the 0.5% theoretical uncertainty. We also calculate the hyperfine quenching rate of the 6s6p P-3(0) state in Hg-199 and Hg-201 and determine its lifetime to be 1.3 and 1.9 s, respectively.