Your sentence needs some fixes. You have several errors with articles and it makes more sense to rearrange things. Instead, let's look at this fixed version:
Please send me only the data related to tomorrow's meeting out of the data I sent you yesterday.
I personally (as a native speaker) would use "from" instead. One of the uses of "from" is to indicate the source of something (definition 3).
But "out of" isn't wrong either. If you look it up, you'll see:
out of: Indicating the source or derivation of something; from
This is, however, only one instance where "out of" is used in the middle of the sentence. There are many, many more:
Get out of my house!
Four out of five doctors recommend our product.
I was sick recently, so I'm feeling out of it.
We're out of milk.