Russell Brand -- Homeless Man Trash Picker-Upper [VIDEO]

Russell Brand's a trash-cleaning machine -- especially after he smashes his SUV into an unsuspecting homeless man's garbage-filled shopping cart -- and TMZ has the video proof.

We broke the story ... Russell accidentally crashed his black SUV into a homeless man's cart yesterday morning in L.A. -- and scrambled to clean up the mess before anyone could see.

No one was injured in the accident and the homeless man went back about his business asap -- but the video footage reveals just how frantic the clean-up effort really was.

The entire clean-up barely took minutes and as soon as the job was complete, Brand hastily jumped into his car and beat a hasty retreat ... leaving no trace behind.