Their people, money and weapons don't vanish and what we see when cartels take a hit income is violence increases and the cartels look to other methods of making income using they're existing tools. Protection rackets and kidnappings are already used as supplemental income, these would only increase.
Now a long approach of gradual decriminalization and legalization may work, with the ability to operate legally the need to utilize violence decreases over time as it's generally bad for business.