I am more familiar with this as "not to mention", though the sense is, I think, the same:
"X, not to say/mention Y" is often used to strengthen the first claim/concept. Example:
Sarah is awful at her job! She never arrives on time, not to say/mention how little effort she makes when she is here.
The fact that 'she never arrives on time' gives good reason for my claim that 'Sarah is awful for her job', even without adding that she makes no effort. By using the 'not to say' clause, we are giving further reason to accept the original claim.
As a point of interest, another similar phrase exists with quite a different meaning:
If I say "X. That is not to say Y", it means that even though my saying X might imply Y, that is not the case.
An example should help:
Sarah is terrible at her job. That is not to say that I think she should be fired; perhaps further training would be a good idea, though.
Here, my first statement (X) might lead you to think that I would advocate Sarah being fired. I want to clarify that I do not feel that way, so I use the 'not to say Y' statement to ensure that the listener doesn't get the wrong idea.
Hope that helps.