The processing stage (i.e., the early semantic representation stage, the late response-selection stage, or both) at which the spatial-numerical association of response codes (SNARC) effect occurs is still controversial. The two-stage processing model hypothesizes that the SNARC effect involves both stages and that different interference factors acting at the two stages might be the core reason for the observed stage flexibility of the SNARC effect. To test this hypothesis, the present study was designed to elicit the SNARC, Stroop (semantic-representation stage related), and Simon (response-selection stage related) effects together in one magnitude comparison task and used the event-related potentials (ERPs) to observe the temporal dynamics of these effects. The behavioral results showed no interaction between the Stroop and Simon effects, while these two effects both interacted with the SNARC effect. Furthermore, the ERP results showed an interaction of the Stroop effect with the SNARC effect for the early sensory P1 component, while the interaction of the Simon effect with the SNARC effect was evident for the late N2 and P300 components. The current study repeatedly verified the independence of Stroop and Simon effects. Most importantly, the temporal-specific interactions among the SNARC effect and the other two stage-related factors provided further evidence to support the two-stage processing model that the SNARC effect involves both the representation and response-selection stages.