Pretty much by working it to death.
Alcohol is broken down by the liver through a series of steps that involve breaking it down into smaller compounds until it winds up as simple sugars. However, some of these intermediate compounds are far more toxic than alcohol. They only last a few seconds until they’re transformed to something else but they still do damage.
Now, your liver is pretty much limited to processing roughly 30 ml of pure alcohol per hour. If there’s more than that, it just keeps passing through the liver on every trip until there’s capacity to process it.
But if you keep the pressure on, the liver tissue eventually breaks down entirely due to the toxic effects, which are magnified by the process of breaking it down and are largely limited to the liver because it tries to protect you from the deleterious effects. As the liver tissue breaks down, it turns to fat.
But this keeps the liver from doing its other jobs, one of which is to break down dead red blood cells so their components can be recycled into new blood cells. One of the by-products of this process is bilirubin which has no biological use and is simply processed by the liver and gall bladder (if you have one) until it’s dumped into your intestines.
However, if your liver is busy with alcohol instead the bilirubin doesn’t break down and it just keeps circulating in your blood, which manifests as this:
Jaundice. This is a good sign your liver doesn’t work anymore.
Let’s face it. Alcohol is a poison and, if you have too much in your system it effects how your nervous system works until it stops working altogether. At that point your heart stops and you die. Your liver tries to prevent this, but at a sacrifice. As I said, the by-products of the process are more toxic, which is why alcohol can make you nauseous - that’s the breakdown products from the liver speaking. The liver takes one for the team to keep your nervous system working. In fact, there’s a drug that prevents the liver from processing these highly toxic by-products, which results in you getting very nauseous - it’s sold to alcoholics to keep them from drinking because even a little makes you very nauseous. This is what your liver has to put up with because you drink to excess.
Your liver is a robust organ and it can handle lots of toxic substances in addition to alcohol, either rendering them harmless or even getting some nutritional value out of them. However, there’s a limit and, if you exceed it on a daily basis, that’s it, that’s all.