My car keeps stalling when I slow down or try to shift. Why?

I have a 2001 Ford Mustang with a manual transmission. When I first start the car, the engine does turn over, but i have to give it a lot of gas and it stays on for a bit. But the minute I go to shift or slow down it stalls… Why is it doing that?

I've been driving stick shift cars for a while so it's not user error… Its the car…

Added (1). I know it opens the valve to let air in…"giving it gas" is just a phrase… Its kind of a no brainer its something in the engine… I'm trying to find out if anyone has any idea what part of the engine is causing this… I think it may be the fuel injector but if its something I can fix at home I'd like to have an idea before pay a ton of money to have it fixed by an over priced mechanic.

It's probably not getting enough gas it could be your tank is near empty and it's dirty or it could be the filter needs to be cleaned or changed

Have you checked the air filter?
Have you checked the throttle body where the butterfly valve is located to see if it is full of carbon?
I would think this is an engine issue… LOL

When you step on the gas when your starting a car its giving air to it not gas but the stalling deal is probably an engine issue.