My wife always does what I say.
My wife always do as I say.
What is the correct sentence? Should I use does or do, when do is not an auxiliary verb?
Yes, it changes to "does", because all lexical verbs acquire "s" at the end in the third-person singular present-tense form:
My wife always does as I say.
My wives always do as I say. (If you live in Saudi Arabia)
This rule is only broken in very rare situations, for instance, in poetry, in order to retain the meter:
Turned are those lights from me, who fondly yet
Past joys, vain loves, and buried hopes regret.
The quoted poem is the only example that I have been able to spot so far. And even here I've been proven wrong: see the comment by StoneyB below.
Hence, this rule is not broken even in poetry.