For revealing the dynamics of partially obstructed breakup of bubbles in microfluidic Y-junctions, the combination of dimensionless power-law and geometric model was applied to study the effects of capillary number, bubble length, and channel angle on the bubble rupture process. In the squeezing process, the gas-liquid interface curve follows the parabolic model. For the evolution of the bubble neck during breakup, the increase of the bubble length, the channel angle, and the capillary number leads to the decrease of the focus distance alpha. The chord m increases with the increase of the capillary number and the decrease of the bubble length, and it would reach the maximum value when the channel angle is 90 degrees. In the fast pinch-off stage during bubble breakup, the bubble's neck curve no longer conforms to the parabolic model so the focus and chord no longer exist. For the evolution of the bubble head during breakup, the value of gamma approaches 1 with the increase of the capillary number and the bubble length, and with the close of the channel angle to 90 degrees. It is found that the quadrilateral model can be applied for the partially obstructed rupture of bubbles in the symmetrical microfluidic Y-junction.