You certainly ***can*** use *to go* in this way, but it's a somewhat informal usage. [ definition 46][1]

> **to go:** Informal. **to say; declare** (usually used in speech)  
 *I asked the clerk for my receipt, and he **goes**, “You don't need it.”*

Many people who think the above example is excessively informal / uneducated will nevertheless accept *as the saying goes* because they've heard it so often (besides which, *as the saying **says*** sounds silly). But it's essentially the same usage.