There has been one reported incidence of liver toxicity that I am aware of - and it was a person who was addicted to Yerba Mate (or, just Mate) like some people are to coffee - drinking several potfuls a day, all day long. On the other hand, there are hundreds of reports, studies and anecdotal stories of Mate being especially healthful to the liver in many different way as well as healthful to various other organs and the immune system, and as a valuable and powerful anti-oxidant.
Studies in Uruguay are giving some indication now of a possible link to some forms of cancer among those who drink Mate heavily - especially those who also are heavy users of the black tobacco popular there. I suspect that pesticides and other pollutants and toxins, may play a part. I also suspect that heavy use and dependency on Mate, which does contain caffeine and other natural stimulants, combined with poor supplementation and nutrition, is a bad combination in the same way that it would be for tea, coffee or any other natural or unnatural stimulant. And, like any form of stimulant, overuse can make you strung out and a bit schitzy.
A great many things in our diets have compounds that can be harmful when consumed regularly in large amounts and in the absence of a healthy lifestyle that would otherwise cleanse and detox the body on a regular basis, supply the proper vitamins, minerals and other nutrients, avoid other toxins, and maintain a robust immune system that is designed to handle the routine toxins and pathogens we all encounter regardless of how or where we live.
If one decides to use Yerba Mate, it would be a good idea to use Mate in moderation and make sure that you buy only good quality organically grown Mate.