No. You don't wash meat before cooking it. Process is this.
Wash your hands for at least 20 seconds
Take out your meat, cut as needed, season/rub meat, do whatever the fuck else you need to do to prep
Wash hands after touching meat or before touching a different type of meat. Otherwise, cross-contamination happens. This is bad, and will make people sick or kill them. In other words: Beef on beef = OK, beef on chicken = NOT OKAY
Cook your fucking meat. Once they are cooked, it doesn't matter if they touch or not.