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You certainly can use to go in this way, but it's a somewhat informal usage. Dictionary.com definition 46

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.