Seismic isolators have been extensively utilized in the field of structural vibration control due to their superior control effectiveness in reducing absolute acceleration responses. However, this effectiveness comes with compromise on large isolating deformation, which may result in various issues, such as pounding and/or unseating damages of bridge decks. To address these issues, negative stiffness enhanced tuned mass damper (NS-TMD) was proposed in the literature, with the aim of minimizing the absolute acceleration while concurrently limiting isolation device deformation. Although previous studies have demonstrated the superior control performance of NS-TMD, there still exist the following unresolved issues: (1) previous studies only focused on a single-objective optimization problem (e.g., seismic response of primary structures), without considering the stroke of NS-TMD during the optimization procedure, which may make the design impractical; (2) the commonly used negative stiffness (NS) elements in NS-TMD, such as the pre-compressed helical springs with revolute joints, suffer from limitations in the operating range near the equilibrium position and are prone to buckling under prolonged high stress during spring rotation. To this end, this study proposes a novel NS-TMD, which consists of a TMD with a curved-type mass block and an NS element based on a cam-roller-spring (CRS) mechanism. The working mechanism of the novel NS-TMD is first introduced, and its mechanical model is formulated. This novel system is then applied to a typical isolated bridge to illustrate its control effectiveness. Equilibrium equations and state space formulations of the system are derived. Subsequently, parametric analysis on NS-TMD is performed, followed by the proposal of a multi-objective optimization strategy to simultaneously minimize the relative displacement of the bridge deck and the stroke of NS-TMD. Finally, the control performance of NS-TMD is systematically evaluated. Numerical results show that the optimized NS-TMD not only reduces the deck displacement of the bridge system (with a maximum reduction ratio of 49.50%) but also decreases its absolute acceleration. Furthermore, NS-TMD can achieve superior control performance in terms of the deck displacement, while limiting the stroke within a reasonable range.