Mixed-anion compounds, which incorporate multiple types of anions into materials, display tailored crystal structures and physical/chemical properties, garnering immense interest in various applications such as batteries, catalysis, photovoltaics, and thermoelectrics. However, detailed studies regarding correlations among crystal structure, chemical bonding, and thermal/vibrational properties are rare for these compounds, which limits the exploration of mixed-anion compounds for associated thermal applications. In this work, we investigate the lattice dynamics and thermal transport properties of the metal chalcohalide, CuBiSCl2. A high-purity polycrystalline CuBiSCl2 sample exhibits a low lattice thermal conductivity (κL) of 0.9-0.6 W/(m·K) from 300 to 573 K. By combining various experimental techniques, including three-dimensional (3D) electron diffraction, with theoretical calculations, we elucidate the origin of low κL in CuBiSCl2. The stereochemical activity of the 6s2 lone pair of Bi3+ favors an asymmetric environment with neighboring anions involving both short and long bond lengths. This particularity often implies weak bonding, low structure dimensionality, and strong anharmonicity, leading to a low κL. In addition, the strong 2-fold linear S-Cu-S coordination with weak Cu···Cl interactions induces a large anisotropic vibration of Cu, which enables strong phonon-phonon scattering and decreases κL. The investigations into lattice dynamics and thermal transport properties of CuBiSCl2 broaden the scope of the existing mixed-anion compounds suitable for the associated thermal applications, offering a new avenue for the search for low thermal conductivity materials in low-cost mixed-anion compounds.