Surface-enhanced Raman spectroscopy (SERS) has emerged as an ultrasensitive molecular-fingerprint-based technique for label-free biochemical analysis of biological systems. However, for conventional SERS substrates, SERS enhancement factors (EFs) strongly depend on background refractive index (RI), which prevents reliable spatiotemporal SERS analysis of living cells consisting of different extra-/intracellular organelles with a heterogeneous distribution of local RI values between 1.30 and 1.60. Here, we demonstrate that nanolaminated SERS substrates can support uniform arrays of vertically oriented nanogap hot spots with large SERS EFs (>107) insensitive to background RI variations. Experimental and numerical studies reveal that the observed RI-insensitive SERS response is due to the broadband multiresonant optical properties of nanolaminated plasmonic nanostructures. As a proof-of-concept demonstration, we use RI-insensitive nanolaminated SERS substrates to achieve label-free Raman profiling and classification of living cancer cells with a high prediction accuracy of 96%. We envision that RI-insensitive high-performance nanolaminated SERS substrates can potentially enable label-free spatiotemporal biochemical analysis of living biological systems.