Like is a preposition. It should be followed by an object to make a prepositional phrase.
As is a conjunction. It should be followed by a clause containing a subject and a verb.
Incorrect: He runs like a gazelle does.
(Like is followed by a clause.)
Correct: He runs like a gazelle.
Correct: He runs as a gazelle does.
This is sometimes confusing because as occasionally is used with elliptical clauses which may resemble prepositional phrases.
Like is never used with clauses in standard English.