Hey Sven,
First things first; I know next to nothing about cutting meat, (other than with knives) but I do know reciprocating saws and I think that cutting meat with one would create a nasty cleaning job, simply because the reciprocating saw cuts on the return stoke and so will pull bits of meat and bone into the front of the tool.
I did a quick google for butchers hand meat saw and found this,
https://store.butchersupply.net/hand-saw-frames-c35.aspx
Here's my google if you want more.
https://www.bing.com/search?q=butchers hand meat saw&pc=cosp&ptag=C8N9923A6EFB831429&form=CONBDF&conlogo=CT3210127
Bit of a funny story; Years ago I worked for a chap in a boat shop, whose Grandaddy had started the business. Grandad felt like he had free use of the shop and tools and one day came in and cut a raw ham in half on the large shop band saw. several days later, it was summertime, we started noticing vast numbers of maggots flooding out of the band saw. Grandson wasn't overly happy with Grandaddy.