Not really. Here's what it means:
not one's cup of tea (informal) - not what one likes or is interested in:
cats were not her cup of tea
Oxford - not my cup of tea
I'd like to ask you if the idiom "It is (not) my cup of tea." means "It is (not) my business."
And do really this idiom still popular nowadays?
Nyota has supplied the definition and I'll just add that it's frequently used in AmE.
***** NOT A TEACHER *****
(1) Of course, this is only my opinion, but I would guess that
this is no longer a popular phrase in the United States.
(2) The last time someone said this to me was about 10 years ago, and
the speaker was a "mature" person -- like me.
(3) And I do not remember ever hearing it on the radio or TV during this
time. Nor have I read it in newspapers or magazines.
(4) I suspect (of course, I do not know) that most young people
(who consider themselves to be "cool") would laugh if you used that
saying. (In fact, is the word "cool" still cool?)
"Groovy", however, since it's no longer mainstream, is used in some hipster circles to show their "authenticity" and affinity with the culture of the 60s. As such, it's a "cool" word.
But if you're not a hipster but, say, an investment banker and you use "groovy", it's no longer "cool"