To address the drawbacks of conventional compliant micro-positioning platforms—namely structural complexity and excessive spatial occupancy—while ensuring a millimeter-scale motion range, high positioning accuracy, and favorable static and dynamic performance, this study proposes and develops a novel 3T1R compliant kinematic pair. The pair transmits displacement through the bending deformation of compliant beams, and, based on this configuration, a new translational compliant micro-positioning platform with three degrees of freedom is constructed, in which a single kinematic pair replaces traditional multi-branch structures. On this basis, theoretical models describing the static and dynamic characteristics of the platform are derived using compliant mechanism modeling methods, and the structural parameters are optimized to improve overall performance. Finite element analysis is subsequently performed to validate the proposed theoretical models. The results demonstrate that the theoretical predictions and simulation outcomes exhibit smooth and consistent agreement. A clear separation is observed between the first three and higher-order natural frequencies, and within a motion range of 1 mm, the parasitic motions and coupling errors in all translational directions are effectively constrained within 0.7%. These findings confirm both the rationality of the proposed compliant kinematic pair and the structural design of the platform, as well as the correctness of the theoretical modeling approach, thereby providing new theoretical foundations and design strategies for the advancement of compliant micro-positioning platforms.