The correct form of tense for the given sentence is 'was chopping'.
We often use 'while' with the past continuous to refer to background events.
Example: While he was working, he often listened to music.
Here, in the given question 'was chopping' should be used because we know that with 'while' the past progressive/continuous tense is used when it refers to background events.
Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
Correct Sentence: The butcher cut his hand while he was chopping meat