While the mechanical disruption of microscopic structures in complex fluids by large shear flows has been studied extensively, the effects of applied strains on the dielectric properties of macromolecular aggregates have received far less attention. Simultaneous rheology and dielectric experiments can be employed to study the dynamics of sheared colloidal suspensions over spatiotemporal scales spanning several decades. Using a precision impedance analyzer, we study the dielectric behavior of strongly sheared aqueous suspensions of thermoreversible hydrogel poly(N-isopropylacrylamide) (PNIPAM) particles at different temperatures. We also perform stress relaxation experiments to uncover the influence of large deformations on the bulk mechanical moduli of these suspensions. All the sheared PNIPAM suspensions exhibit distinct dielectric relaxation processes in the low and high frequency regimes. At a temperature below the lower consolute solution temperature (LCST), the complex permittivities of highly dense PNIPAM suspensions decrease with increase in applied oscillatory strain amplitudes. Simultaneously, we note a counter-intuitive slowdown of the dielectric relaxation dynamics. Contrary to our rheo-dielectric findings, our bulk rheology experiments, performed under identical conditions, reveal shear-thinning dynamics with increasing strain amplitudes. We propose the shear-induced rupture of fragile clusters of swollen PNIPAM particles to explain our observations. Our work illustrates that rheo-dielectric studies have enormous potential for providing deep insights into the length scale-dependent dynamical properties of complex systems such as dense suspensions and soft glasses.