There seem to be two ways of taking memory out of the mind in Harry Potter
One is what Prof. Slughorn did, that is, give Harry a copy of his real memory of telling Tom Riddle about Horcruxes. It is not explained directly in the book that what Harry got was a copy and not the real piece of memory in his mind, but I think that much can be implied (since Prof. Dumbledore has a tampered copy of the same thing, and prof. Slughorn still seems to retain the original memory with him, showing that it is possible to make a copy. There is no reason for him not to give Harry just a copy as well)
Another seems to be what Professor Snape did; remove his memory of having insulted Lily into the pensieve so that if Harry accidentally breaks into his mind during legiiimency class, he won't be able to see that part of Snape's mind. Again, it isn't directly explained if what Snape removed was just a copy or the real thing, but I think it can be implied from the narrative it was the real piece of memory from his mind.
So in effect, is that memory now gone from his head?
Does this now mean Snape does not have any recollection of that event what-so-ever? If someone were to tip the contents of the pensieve away, or in some other way bottle it up somewhere else so that Snape cannot take it back, he will never know it had ever happened? Once he takes it out and puts it in the pensieve, is all that he knows now is that he has pulled out some memory from his mind and needs to put it back later?