Severe Acute respiratory syndrome coronavirus (SARS-CoV-1) attaches to the host cell surface to initiate the interaction between the receptor-binding domain (RBD) of its spike glycoprotein (S) and the human Angiotensin-converting enzyme (hACE2) receptor. SARS-CoV-1 mutates frequently because of its RNA genome, which challenges the antiviral development. Here, we performed computational saturation mutagenesis of the S protein of SARS-CoV-1 to identify the residues crucial for its functions. We used the structure-based energy calculations to analyze the effects of the missense mutations on the SARS-CoV-1 S stability and the binding affinity with hACE2. The sequence and structure alignment showed similarities between the S proteins of SARS-CoV-1 and SARS-CoV-2. Interestingly, we found that target mutations of S protein amino acids generate similar effects on their stabilities between SARS-CoV-1 and SARS-CoV-2. For example, G839W of SARS-CoV-1 corresponds to G857W of SARS-CoV-2, which decrease the stability of their S glycoproteins. The viral mutation analysis of the two different SARS-CoV-1 isolates showed that mutations, T487S and L472P, weakened the S-hACE2 binding of the 2003-2004 SARS-CoV-1 isolate. In addition, the mutations of L472P and F360S destabilized the 2003-2004 viral isolate. We further predicted that many mutations on N-linked glycosylation sites would increase the stability of the S glycoprotein. Our results can be of therapeutic importance in the design of antivirals or vaccines against SARS-CoV-1 and SARS-CoV-2.