Clutch moments happen. Sometimes from the unlikeliest players, like (ugh) Bucky Dent or Aaron Boone or Francisco Cabrera.
And certainly Papi. But I just think of Papi as a great hitter who excelled in and out of the clutch.
To me, "clutch hitter" seems more like a reputation based on individual successes and ignoring the failures. Earlier, you mentioned Yaz in 1967. I wasn't born when that happened, but if you ask people my age about how clutch Yaz was, everyone remembers him popping out to Graig Nettles with the tying run on third. And for that, he is remembered as "unclutch."
For the record, that is a laughably bad view of Yaz. The guy was like 39 years old when that happened and had already had a great career of successes and failures in every situation imaginable. But he was remembered for that by my generation (outside of me) for a long time...