The colloidal stability of surfactant-dispersed single-wall carbon nanotubes (SWCNTs) is determined by microscopic physicochemical processes, such as association, partitioning, and adsorption propensities. These processes can be controlled by the addition of solutes. While the effects of cations on the colloidal stability of SWCNTs are relatively well understood, little is known about the effects of anions. In this study, we examined the effects of anions on the stability of SWCNTs dispersed by sodium dodecyl sulfate (SDS) using sodium salts, such as NaCl and NaSCN. We observed that the intensity of the radial breathing mode Raman peaks rapidly decreased as the salts were added, even at concentrations less than 25 mM, indicating the association of SWCNTs. The effect was stronger with NaSCN than NaCl. We propose that the association of SWCNTs was caused by thermodynamic destabilization of SDS assemblies on SWCNT surfaces by these salts, which was confirmed through SWCNT separation experiments using aqueous two-phase extraction and gel chromatography. These results demonstrate that neutral salts can be used to control the colloidal stability of surfactant-dispersed SWCNTs.