Is it "to shave my beard" or "to shave my face"?

I shaved my beard this morning.
I shaved my face this morning.

Which one is the correct sentence?

They are both reasonable sentences; they mean slightly different things. But the most common and idiomatic thing to say would be simply

I shaved this morning.

If you are male, then unless context explicitly suggests otherwise, this will be taken to mean that you shaved your face. (If you’re female, then legs and/or armpits will probably be the default interpretation.)

I shaved my face this morning.

means essentially the same, and is a bit less idiomatic, but would be used to clarify the meaning if context could suggest shaving something else — if, for instance, you also regularly shave your head, then you might want to use this one.

I shaved my beard this morning.

is again less common, and more specific. You would be more likely to use this if you sometimes grow a significant beard, and less likely to use it if you shave every day.

First, That's beard.

Second, you can use both.

See the Examples:

I wish he'd shave off that awful beard.

I've decided to shave off my beard.

And for face:

Before using the device, you should learn how to shave your face.