The SARS-CoV-2 spike protein (S) is the sole viral protein responsible for both viral binding to a host cell and the membrane fusion event needed for cell entry. In addition to facilitating fusion needed for viral entry, S can also drive cell-cell fusion, a pathogenic effect observed in the lungs of SARS-CoV-2 infected patients. While several studies have investigated S requirements involved in viral particle entry, examination of S stability and factors involved in S cell-cell fusion remain limited. We demonstrate that S must be processed at the S1/S2 border in order to mediate cell-cell fusion, and that mutations at potential cleavage sites within the S2 subunit alter S processing at the S1/S2 border, thus preventing cell-cell fusion. We also identify residues within the internal fusion peptide and the cytoplasmic tail that modulate S cell-cell fusion. Additionally, we examine S stability and protein cleavage kinetics in a variety of mammalian cell lines, including a bat cell line related to the likely reservoir species for SARS-CoV-2, and provide evidence that proteolytic processing alters the stability of the S trimer. This work therefore offers insight into S stability, proteolytic processing, and factors that mediate S cell-cell fusion, all of which help give a more comprehensive understanding of this highly sought-after therapeutic target.