Experimental studies on a kind of thermotropic liquid crystalline polymer (TLCP) containing 30% p-hydroxybenzoic acid (HBA), 35% hydroquinone (HQ), and 35% sebacic acid (SA) in mole fractions and its nanocomposite (TC3) containing 3.0 wt% organoclay are reported. The structures and dynamics of shear-induced phase separation and the effects of these structures on the macroscopic rheological properties of the nanocomposite are characterized under different shear conditions at 190 °C, which is in the nematic transition region of TLCP. The molecular level interactions between organoclay and TLCP molecules form a percolated-network structure in the composite, causing the composite to display complex viscosity with more than two orders of magnitude greater than that of TLCP in linear regions. However, such a network structure is easily destroyed in steady shear deformation, and it does not recover. Polarized optical microscopy (POM) equipped with a Cambridge shear system and transmission electron microscopy (TEM) confirm a shear-induced phase separation phenomenon during steady shear deformation. Two phases are observed in POM and TEM, with TLCP-rich and organoclay-rich phases. Steady shear at a small shear rate is effective to separate the two phases for characterizations.