Online records for the Athens-Clarke County jail show Beal and Cox were charged with misdemeanor possession of less than one ounce of marijuana. Each posted $1,000 bond.
"I'm obviously extremely disappointed," Georgia coach Kirby Smart said after practice Tuesday. "I've obviously done a poor job with this group of connecting and making sure they listen and understand things."
Cox, a rising sophomore, played in 13 games as a freshman, including a start in the Allstate Sugar Bowl. He had 20 total tackles and one sack for the season.
Beal, also a rising sophomore, made 15 tackles in 11 games in 2018.
"We have policies and rules in place; these guys violated those policies and rules, and they will serve the punishment that they deserve for it, and I hate the decision they made," Smart said. "They have to learn as young men that you can't break the rules, you can't break the law."
The arrests come a week after Georgia receiver Tyler Simmons and cornerback Tyrique Stevenson were charged with disorderly conduct after allegedly fighting with bar employees at the Cloud Bar.
Also, linebacker Jaden Hunter was arrested March 20 on charges of driving with a suspended or revoked license and stopping, standing or parking in a prohibited area. In addition, safety Latavious Brini was charged with misdemeanor simple battery in February.
Smart said the off-the-field issues fall on him.
"We're going to do a great job of moving forward to get these guys in the right place to make the right decisions," he said.