Glencore also said in a statement it was "still evaluating" its contracts with the Russian company, but it announced it would now not be going through with a planned deal with EN+, which owns a controlling stake in Rusal.
"Mr Glasenberg has resigned from his position as a director of Rusal," the statement said.
The decisions came a day after Rusal saw its share price fall over 50 percent Monday on the Hong Kong stock exchange, where it is listed. It fell an additional 8.7 percent Tuesday.
Glencore also saw its shares dip 3.4 percent Monday on the London FTSE stock exchange, though its shares were back up 2.0 percent Tuesday.
The moves came after the United States on Friday announced a slew of sanctions targeting Russian oligarchs close to President Vladimir Putin.
Among the business magnates hit by the punitive measures is Oleg Deripaska, who controls Rusal and EN+.
The sanctions follow a diplomatic crisis sparked by the poisoning of former spy Sergei Skripal.
Tensions between Russia and the West are also soaring over Moscow's intervention in the Syrian conflict, and over an alleged chemical attack targeting a rebel-held area near Damascus.
Russian central bank chief Elvira Nabiullina said on Tuesday that the country's economy could withstand the latest US sanctions, even as the rouble continued its spectacular plunge against the dollar and the euro.