I would guess (hope) that whatever database they track the horse deaths in there are fields for trainer and therefore that data can be gathered. However to really assess that data there is likely other data that needs to be merged into that database.
So if Trainer A on average has 25 horses in training per day 365 days a year and has 4 horses that break down/euthanized every year on average that is different statistic than Trainer B who has 10 horse in training for just the Fingerlakes meet and averages 2 horses euthanized every year on average. Trainer B has less deaths per year but a MUCH higher percentage of his horses in training died compared to Trainer A. There may need to be a way to compare number of death per training days or per starts or some other baseline.
I am going to preface this with I know NOTHING about racing. However I can see a potential difference in mortality stats on a trainer that obtains a lot of their horses in low level claiming races where they may not have that horses full xrays and all of his vet treatment history available. They may be more likely to unknowingly inherit an issue caused by other trainers or just lack of available information.
Compare that to a Bob Baffert who primary runs stakes horses who have come through high end sales so have lots of x-rays available before they start to race. Then they spend the majority of their racing life with one trainer who has either their whole vet history or at least the overwhelming majority of that history. Even if they switch to a different trainer my guess is that the vet history and treatment history is better documented and more likely to transfer to the new trainer/owner.
The trainers that primarily train stakes horses may be more likely to have owners that can afford to have a PET scan, bone scan , MRI or ultrasound if the horse takes two funky steps rather than an owner that the horse really needs to be lame or longer term NQR before advanced diagnostics would be considered.
Comparing different trainers based out of different tracks and different footing may not be possible if one of the track footings is contributing to breakdowns. So even if you use a baseline of number of breakdowns per training days across the country if a particular track has a higher incidence of breakdowns per training days then comparing trainers from that track to another track may not give the whole picture.
Straight up comparing the number of deaths per year per trainer likely is not as straight forward as it seems on the surface.
Disclaimer: My husband does data mining and data evaluation for a pharmaceutical company so I have a little bit of insight from talking to him on how much can go into comparing evaluating complicated data points.