I have no idea. So I decided to ask.My motivation is that it would be an interesting juxtaposition of violence and non violence.
It is hard to answer your question.
Are you asking about the biggest empire that never ever had capital punishment during its entire existence as an empire? The problem with that would be defining what counts as an empire and also in some cases defining how long an empire lasted.
It seems to me that the longer an empire lased, the more likely it would be to change whether it had capital punishment. If you question is about an empire which never had capital punishment during its entire duration, then the shorter an empire lasted the better. An empire which lasted for a really short time might have had capital punishment the entire time or might have been without capital punishment the entire time. So short lasting empires would be a logical group of candidates to search for empires without capital punishment for their entire duration.
Here is a link to a thread about various empires or states that are often classified - accurately or not - as empires and which lasted for short periods of time.
In post number one I list 18 empires and "empires" which lasted for no more than 27 years.
Several other empires and "empires" were suggested, and in post number twelve on page two I gave a revised list of 20 empires and "empires" that lasted between 27 years and 12 days.
In most number thirteen I list 21 empires and "empires" that lasted between 27 years and 12 days in my final list.
So perhaps a study of the laws of those 21 empires and "empires" might find one or more without the death penalty. if any of them were without the death penalty (which I doubt) the largest of them would be the largest empire without the death penalty. Unless some larger empire lasted for more than 27 years without the death penalty, which I doubt.
But if you are asking for the largest empire which ever abolished the death penalty, even if that empire later restored the death penalty, then you have some luck.
According to Wikipedia's List of Largest Empires by land area at their greatest extent, number 22 on the list is the Tang Empire, the empire of the Tang Dynasty, at its greatest extend in AD 669 or 715. In those eras the Tang Dynasty ruled 5,400,000 to 10,760,000 square kilometers or 2,080,000 to 4,150,000 square miles.
Emperor Xuanzong (reigned 712-756) abolished the death penalty in China in 747, but it was reinstated in 759 due to the bloody An Lushan Rebellion that killed millions in 755-763.
The size of the eastern section of the Roman Empire, the so called "Byzantine" Empire, fluctuated greatly over time. After the defeat at Manzikert in 1071, the Empire lost a lot of land to invaders. In 1097 the size of the Empire was about 555,000 square kilometers, but by 1143 it had regained much lost territory and was up to 950,000 square kilometers.
This increase of about 1.7117 times in the size of the Empire in only 46 years was due to the leaderships of the Emperors Alexios I Komnenos (reigned 1081-1118) and John II Komnenos (reigned 1118-1143).
Emperor John II Komnenos (r. 1118-1143) fought many wars in which many thousands of people were killed, but he was said to have never executed or mutilated any Roman subjects as legal punishment during his 25 year reign.
Present day Japan has an area of 377,973 square kilometers or 145,936 square miles. Medieval Japan didn't include the island of Hokkaido with an area of 83,423.84 square kilometers or 32,210.12 square miles, so Medieval Japan would have had an area of 294,549.16 square kilometers or 113,725.88 square miles, or less.
The death penalty was abolished or suspended in Medieval Japan for over 300 years from some time in the 9th century until the Hogan Rebellion in 1156.
The oldest country I know which abolished the death penalty was Magadha under the Gupta Dynasty (at latest under Chandragupta II who reigned from 375 - 413/415). The Chinese monk Faxian (he traveled from 399 - 412) mentions that even high treason was only punished by cuting the right hand.
Post number 58 on page 6 of: https://historum.com/threads/which-was-the-first-country-to-abolish-the-death-penalty.124922/page-66)
These are the only examples I know of where states which might be classified as empires abolished or suspended the death penalty, and none of them did so for their entire existence.
I think that the OP is incorrect in supposing that an empire without the death penalty would combine violence and nonviolence any more than a nation or other non empire without the death penalty would. That supposes that empires are more violent than non empires, and that seems to be without proof.