He didn't shoot his arm off. Maybe if it was a 12 shotgun loaded with buckshot he might have or forced it to be amputated. That would have been even better.
I used to have some .410 shot shells that had a few 000 buck in them. You could put that in a .45 revolver and if you had to shoot someone with it, that would definitely ruin their day. ;)
Lennon deliberately chose to obfuscate the meaning of his signature song, even the title Strawberry Fields Forever was, in its day, controversial and ambiguous. Lennon simply took the name from a Salvation Army children's home in Liverpool called Strawberry Field (singular) which existed until 2005. The site has now been closed since 2011.
According to Wikipedia, Lennon's iconic lyric was inspired by a childhood memory
For the refrain, [...]: the words "nothing to get hung about" were inspired by Aunt Mimi's strict order not to play in the grounds of Strawberry Field, to which Lennon replied, "They can't hang you for it."
In other words, the young John Lennon knew full well he couldn't be arrested or given the death penalty for playing on the premises. The death penalty in the UK was suspended in 1965, one year after the last two men had been hanged in Britain, and five years after The Beatles had already been formed. The verb hang, when it refers to being killed by means of a rope tied to one's neck, is regular but it is not uncommon for native speakers (and in some dialects, I suppose) to use the irregular past tense hung in speech and in writing.
In fact, in verse two an even more obscure lyric, whose meaning never really caught on, is the following.
No one I think is in my tree, I mean it must be high or low
Does the tree refer back to hanging, or as John Lennon asserted in 1980 to his feelings of alienation, and “Therefore, I must be crazy or a genius — ‘I mean it must be high or low,’ ”