Stacking two-dimensional (2D) van der Waals (vdW) materials in a layered bulk structure provides an appealing platform for the emergence of exotic physical properties. As a vdW crystal with exceptional plasticity, InSe offers the opportunity to explore various effects arising from the coupling of its peculiar mechanical behaviors and other physical properties. Here, we employ neutron scattering techniques to investigate the correlations of plastic interlayer slip, lattice anharmonicity, and thermal transport in InSe crystals. Not only are the interlayer slip direction and magnitude well captured by shifts in the Bragg reflections, but we also observe a deviation from the expected Debye behaviour in the heat capacity and lattice thermal conductivity. Combining the experimental data with first-principles calculations, we tentatively attribute the observed evidence of strong phonon-phonon interactions to a combination of a large acoustic-optical frequency resonance and a nesting effect. These findings correlate the macroscopic plastic slip and the microscopic lattice dynamics, providing insights into the mechano-thermo coupling and modulation in 2D vdW materials.