Dimensionality is a fundamental component that can have profound implications on the characteristics of physical systems. In cell biology, however, the majority of studies on cell physical properties, from rheology to force generation to migration, have been performed on 2D substrates, and it is not clear how a more realistic 3D environment influences cell properties. Here, we develop an integrated approach and demonstrate the combination of mitochondria-tracking microrheology, microfluidics, and Brownian dynamics simulations to explore the impact of dimensionality on intracellular mechanics and on the effects of intracellular disruption. Additionally, we consider both passive thermal and active motor-driven processes within the cell and demonstrate through modeling how active internal fluctuations are modulated via dimensionality. Our results demonstrate that metastatic breast cancer cells (MDA-MB-231) exhibit more solid-like internal motions in 3D compared to 2D, and actin network disruption via Cytochalasin D has a more pronounced effect on internal cell fluctuations in 2D. Our computational results and modeling show that motor-induced active stress fluctuations are enhanced in 2D, leading to increased local intracellular particle fluctuations and apparent fluid-like behavior. 