Yes, indeed there are .005" thick very very thin saw blades available now-a-days.
Use the clean link just below
https://www.amazon.com/vdp/0da84c820...f=dp_vse_ibvc0
A little consideration and practice has resulted in some ogive deep .005" wide HST like cuts on a jacketed slug for a 350 Legend.
https://www.amazon.com/dp/B07RTBPL62...roduct_details
https://www.amazon.com/dp/B07GVNS8F1...roduct_details
Future thoughts lead me towards trying to mount this blade on a variable speed oscillating multi-tool to make the cuts much easier to accomplish in bulk.
Cutting jacket and lead by hand is surprising fast at 2 min. per cut, with the resulting swarf being a lead and oil paste similar to cream cheese in consistency. An osculating tool mounted cutter could get the job done in 10-20 seconds per cut.
Some fixturing could easily remove half of this "fumble to get it right" time.
(yes, you do have to oil the blade to keep it from leading up on you).
Please note the incredibly fine cut is barely visible in this picture .... I had to blacken the cuts so yo could see them at all.
Note that the .005" wide cut also tends to close up on itself after the lead and jacket tension relaxes for a few minutes.
You do need a small cone form on the tip of the bullet to start the petals to moving to "open the bullet up".