The spin mixing process of a radical pair in a micelle in a low magnetic field is investigated by transient absorption detected MARY spectra. In a system comprising the radical pair generated by photoreaction of 2-methyl-1,4-naphthoquinone in sodium dodecylsulfate micelle, two techniques were applied: time resolved MARY spectra and pulsed MARY spectra. In order to analyse the results, a practical calculation method that lends itself to the simulation of experimental results has been developed. In the calculation, a semi-classical model was used for the evaluation of the hyperfine mechanism (HFM) in the single-site Liouville equation in which one can take spin relaxation and dephasing phenomena into account. The interrelation between the HFM and relaxation mechanism (RM) was discussed. A new insight into the HFM induced spin mixing process, which is assisted by fast spin dephasing phenomena, is proposed. This mechanism is important for the MARY spectral shape and connects the HFM and RM smoothly.