The effects of premixedness degrees on combustion instabilities of separated dual-swirl flames have been investigated experimentally in the Beihang Axial Swirler Independently Stratified (BASIS) burner. The degree of premixedness is modulated by the fuel split between two injection positions in the outer stream. In the spectra of pressure oscillations, both the frequency and amplitude are positively correlated with fuel split ratios under partially premixed conditions, and the mode transition between perfectly and partially premixed conditions has been observed. The location of perfectly premixed flames shows no obvious variation at different phase angles, only with a slightly wrinkling of the flame surface along the shear layer. Under partially premixed conditions, however, the flame is found to feature a large-scale periodic convective motion, accompanied by the obvious variation of heat releases due to the equivalence ratio oscillations. The local Rayleigh index map compares the thermoacoustic driving factors under perfectly and partially premixed conditions. The development of above convective motions under partially premixed conditions is explained by combining the variations of pressure oscillations and heat releases. An analysis of the thermoacoustic network and convective path is applied to explain the cause of the mode transition. The results show that the appearance of equivalence ratio oscillations and the elongated convective path under partially premixed conditions brings a longer delay time of the flame response, which could be the reason for the mode transition.