Can you cut an arm off with a meat cleaver? In the case of Limehouse, absolutely. He kept his tools sharp and he's a big guy.
If you need proof of that then look no further then the Rwanda genocide of the 90's. Thousands of people lost limbs to rusty machetes and a lot of it was captured on film by reporters as it happened.
If you want something more poetic and less horrific as an example then the legends about the katana and it's sharpness measured in bodies is also mostly true and they were regularly tested by their ability to cut through human bodies and limbs in one swing.
edit: and for related damage check out the ARMA archive of their sword testing against carcasses and materials.http://www.thearma.org/Videos/NTCvid...dmaterials.htm