The short answer is that doing procedures on dead animal tissue is totally fine, legal, aboveboard, ethical, etc. Your adcom will likely want to know about your research. The ethical questions surround how the mice were treated up until and including method of euthanasia. Since it sounds like you will just be given live mice right before your procedure, the only ethical concern you are likely to encounter is doing the euthanasia in an approved way.
Likely before you start the job you will have to watch some videos or go to a seminar about animal research and lab safety (blood borne pathogens, etc.), and although your PI may forget to send you to this couple of hours of training, I think something like it is mandatory everywhere. You will learn that you can basically do whatever you want to invertebrates, but for invertebrates there are some restrictions and there is almost always something like an Institutional Review Board (the one for animals is likely called the IACUC), which is something internal to the school which approves of research proposals. There are published guidelines (various national groups or you school may have its own) on how to treat animals, what to feed them, how to euthanize them, how/when to check them for diseases, how to make sure they are not suffering, how many per cage, etc. In order for your PI to be allowed to host the animals there and do research he/she presumably did tons of paperwork agreeing to follow various protocols and then got the IACUC (other professors, maybe some veterinarians, ethicists, I don't know exactly, but some peeps at your school) to agree to the protocols.
In order for your PI to have gotten money in the first place he/she likely included wording in grant proposals that they were going to follow XXX protocol for animal care and humane treatment, and then when they want to get the research published in a journal, they will also have to include a statement in the paper about how the animals were cared for, method of euthanasia, etc. following XXX protocol again. If someone is not following ethical treatment guidelines and is lying about it, then that is an even bigger breech of professional ethics.
Previously dead animal tissue though is fine for you to do whatever you want with, bounded by your own imagination and moral compass. You can go to a butcher to get pig feet to practice suturing or tendon repair. You can dissect a fetal pig. You can dissect a cow eye or a cow heart. You can get a cow liver with the gallbladder attached and then try to remove the gallbladder using laproscopic tools. You can buy formalin fixed sheep brains and section them. You can filet a fish and cook it for dinner. Whatever you want.
Note by ethics here I mean legal/institutional/professional sorts of ethics. You personally may have very strong feelings about things which differ. That's a point for different discussion. In medical training you are definitely told that certain things are ethical and certain things aren't, and you are tested on these on your various medical boards as they are professional ethics. In your own heart, you may have very different personal opinions, but you can potentially get in trouble for not following the proscribed ethics.
Some people don't like animal experimentation at all, and I know that some people have been traumatized a bit by being involved. Other people aren't bothered at all and enjoy it and like that they are advancing science.
