Oscillatory rheology, at both small (SAOS) and large (LAOS) amplitude, was performed to measure the dynamic response of a soft-solid, formed on dispersing colloids into a thermotropic nematic liquid crystal at volume fractions φ > 18%. Due to weak homeotropic anchoring of nematogens at colloid surfaces, a Saturn-ring defect-line, known as a 'disclination', encircles each particle and entangles with neighbouring Saturn-ring disclinations [1]. We present the first experimental investigation of the yielding behaviour of the resulting gel to reveal the underpinning physics. Results reveal the frequency response of the composite is independent of the volume fraction φ ; an indication that the dispersed phase simply increases the density of disclinations spanning the composite without further effect. Beyond the linear viscoelastic regime (LVR), LAOS experiments indicate the composite is an elastoplastic fluid exhibiting both strain-hardening and shear-thinning behaviour, with Chebyshev coefficients e 3 > 0 and ν 3 < 0 respectively. We deduce that the disclination density n is constant until the strain amplitude is sufficient to break disclinations leading to shear-thinning behaviour beyond the LVR. A simple theory is introduced revealing that the Ericksen number E r determines the onset of flow, when E r > 1, generating a strain-hardening response since the Frank elasticity resists reorientation of molecular alignment within confined nematic domains. Above a critical frequency ω c the loss modulus G increases slowly due to enhanced viscosity within confined nematic domains, G ∝ ω 1/2 [2]. Observation of this behaviour in a small-molecule nematic solvent provides insights into the physics of flow behaviour in other, more complex, defect-mediated liquid crystalline structures exhibiting similar properties [3][4][5].