Needless to say, it depends on the type of yerba mate. However, in general terms, yerba mate has less caffeine than coffee but more than tea. Some of the brands, like Meta Mate, clarify it in their labels, so you can buy based on your preference.
While coffee has approx. 95mg per cup, studies have found that there is approx. 78 mg of caffeine per cup of mate. A cup of mate, according to Mazzafera, is 150 ml, so by drinking 0.5 L of water, you would be having 260 mg of caffeine (almost 3 cups of coffee).