Green’s Dictionary of Slang

saw n.2

[? their ‘rough/sharp edges’]
[1940s] (US black)

1. a woman, esp. when a nag.

2. the landlady of a cheap rooming house.

SE in slang uses

In compounds

sawbones (n.)

[mid-19C+] a doctor, a surgeon.

sawbox (n.)

[1930s–60s] (orig. US black) a cello.

In phrases

hand-saw (n.) [Partridge suggests that -fencer sfx, i.e. seller, should be assumed]

[mid-19C] a street seller of cutlery, razors and knives.

old saw (n.) [? her nagging saws away at a man]

[late 19C–1940s] (US black) one’s wife.