"Uncle Rufus grew his nose,
Threw away his circus clothes"
His nose was his distinguishing characteristic, his individuality. "Circus clothes" refers to his previous role as the clown of the group and also to the images of the past which the group's members now sought to renounce (the costumes worn on the Sgt. Pepper album cover).
"Cousin Silas grew a beard,
Drew another flask of weird"
The former Beatle who became known for the influence of eastern religion ("weird" to westerners) in his work.
"Nasty Jonah grew a wife,
Judas drew his pruning knife."
The further attempts of the other two Beatles to distinguish themselves from the group (establish a new image). Judas' pruning knife represents his cutting himself off from the other members, in effect, disbanding the group.