We propose an algebraic approach to elucidate the dynamic characteristics of triaxial rotor modes in nuclei by mapping a triaxial rotor Hamiltonian to the interacting boson model one within a finite-N framework. Our method unveils striking features not observed in conventional modes, exemplified by the B(E2) anomaly, characterized by B(E2;41+→21+)/B(E2;21+→01+)<1. Using specific examples, we demonstrate that the peculiar properties of low-lying states in both neutron-rich and neutron-deficient Os nuclei can be comprehensively understood through the proposed Hamiltonian, which incorporates both rigid and soft triaxial rotor modes. This algebraic method not only offers fresh insights into triaxial dynamics but also showcases its capability in uncovering emergent exotic collective modes in nuclear structure.