A bandsaw (or “band saw”) has nothing to do with a musical band, but there are jokes. This riddle was posted on Reddit—Dadjokes on April 28, 2019:
 
Q: What is the best way to cut a musician into tiny pieces?
A: With a band saw.
   
Similar puns had been used earlier. “And when we all play together, like fine musicians should, we use a bandsaw” was posted on the newsgroup rec.music.folk on April 13, 1993. “Hey! How does a group of musicians cut through something???........a band saw” was posted on Twitter by Voigt Music Center on September 11, 2014. “When woodworking: Musicians prefer the bandsaw. While hackers prefer the hacksaw” was posted on Twitter by ʎxɐlɐפ pǝɯǝɥʇ oʇuoɹd on October 30, 2018.
   
     
Wikipedia: Bandsaw
A bandsaw (also written band saw) is a power saw with a long, sharp blade consisting of a continuous band of toothed metal stretched between two or more wheels to cut material. They are used principally in woodworking, metalworking, and lumbering, but may cut a variety of materials. Advantages include uniform cutting action as a result of an evenly distributed tooth load, and the ability to cut irregular or curved shapes like a jigsaw.
       
Google Groups: rec.music.folk
Musical saws?
David Kassover
4/13/93
In article <1993Apr13…@cbnewsd.cb.att.com>

.(JavaScript must be enabled to view this email address) (william.b.paulson) writes:
>The kind of saw depends on what sort of music you’re playing -
>Irish tunes need a jig saw, rounds a circular saw, C tunes
>obviously use a C-saw.  Psychotherapists generally recommend coping
>saws.
 
Oh, all right.  This post set my teeth on edge;  It takes a worried man to use a fretsaw.
 
Those who are good at it use a skilsaw; nasty ones use a sidewinder, but troglodytes use a wormdrive.
 
If one wraps one’s music into tubes, one can use a scrollsaw.
 
And when we all play together, like fine musicians should, we use a bandsaw.
   
Twitter
knife f5
@cosminaut
Disposed of the musicians’ corpses using the bandsaw
5:41 AM - 3 Jan 2014
 
Twitter
Voigt Music Center
@VoigtMusic
Hey! How does a group of musicians cut through something???........a band saw.
3:09 PM - 11 Sep 2014
     
Twitter
˙ʎxɐlɐפ pǝɯǝɥʇ oʇuoɹd
@_pronto_
When woodworking: Musicians prefer the bandsaw.
While hackers prefer the hacksaw.
4:04 PM - 30 Oct 2018
 
Reddit—Dadjokes
Posted by u/wmyspr April 28, 2019
What is the best way to cut a musician into tiny pieces?
With a band saw.
bananastasia90
You shred him with his “axe” !?!
 
Twitter
keepingitcreel
@Keepingitcreel
What is the best way to cut a musician into tiny pieces? With a band saw.
12:15 PM - 28 Apr 2019