What does the church do with tithing?
Nothing. Or close enough to it that it makes no difference.
Tithing was supposed to be for the running of the Church. A prophet even talked about a time when tithing wouldn't be necessary. That time is long past. The church could sustain itself forever on the interest from what they have hoarded. They don't need to bully people into paying as much as possible.
So many members lack good savings for retirement or college or even a rainy-day because of the idea that they must give 10% of everything they have. And then the Church just sits on it and lets it earn interest. Charity giving and service mostly come from other sources, like Fast Offerings and volunteers.
No one really knows... and that is a problem. I still give a minimum of 10% of my income but choose charities which are effective and transparent. (see GiveWell.org if interested)
The church builds buildings, pays GA salaries, funds the CES system, and buys stock with tithing.