Novel Coronavirus or SARS-CoV-2 has received worldwide attention due to the COVID-19 pandemic, which originated in Wuhan, China leading to thousands of deaths to date. The SARS-CoV-2 Spike glycoprotein protein is one of the main focus of COVID-19 related research as it is a structural protein that facilitates its attachment, entry, and infection to the host cells. We have focused our work on mutations in two of the several functional domains in the virus spike glycoprotein, namely, receptorbinding domain (RBD) and heptad repeat 1 (HR1) domain. These domains are majorly responsible for the stability of spike glycoprotein and play a key role in the host cell attachment and infection. In our study, several mutations like R408I, L455Y, F486L, Q493N, Q498Y, N501T of RBD (319-591), and A930V, D936Y of HR1 (912-984) have been studied to examine its role on the spike glycoprotein native structure. Comparisons of MD simulations in the WT and mutants revealed a significant destabilization effect of the mutations on RBD and HR1 domains. We have investigated the impact of mapped mutations on the stability of the spike glycoprotein, before binding to the receptor, which may be consequential to its binding properties to the receptor and other ligands.