What is the largest big cat?

Largest natural big cat is the Amur (Siberian) tiger.

However, if a male lion and a female tiger breed they produce a Liger, which is bigger. This does not happen naturally in the wild as tiger and lion ranges do not overlap. There are several Ligers and Tigons (female lion x male tiger, not as big as a Liger) in captivity. Just because ligers are a cross breed does not make them unnatural because unless we as humans forcefully indoce the DNA into the future mother then it will be natural because the parents are chosing to mate with each other. Even though the Liger and Tigon are currently only breed in captivity scientist know believe that because there used to be a species of lion that lived with tigers that there is a possibility that they did mate however the liger or tigon offspring would one not be able to hunt do to enormous size but also because they would be killed while the mother would try to give birth to the huge cubs. So in the wild the largest cat is the Amur or Siberian tiger.
The Siberian tiger is the largest species of cat in the world being 3.70 m long and weighing 350 kg. But the liger is not called a species but is a mixture of lion and tiger their 14 ft long and weigh 410 kg. The largest recorded cat was a liger in 1973 weighing 798 kg.
The Tiger
the Siberian Tiger is the largest living cat.
w.r.t. overall body length it was the American Lion- Panthera Leo atrox.

w.r.t. body mass it was a Sabre toothed cat called Smilodon populator weighing more than 550 kg.

Both are now extinct.