I don't want to kill any more mice, but my advisor insists that I must in order to get my PhD

tonysdg asked in a comment

Can you talk to the department head? Or even better, a university ombudsperson (aka a neutral 3rd party who can discuss your options with you)?

and you replied

I don't know - I'm studying in Germany and I can't speak German.

While it might be a good idea to learn German, you most probably don't have to know German to contact your university's ombudsperson.

Universities tend to be very international environments, and English being the predominant language in middle and western European international research, the ombudsperson is likely to know English and maybe even some other foreign languages. If they don't (or if they don't know English well enough), they can probably get hold of a trustworthy interpreter/translator.

More importantly, I absolutely cannot do anything that results in my PhD coming to an end. If my supervisor gets in trouble, it hurts both of us.

Similar to medical practitioners, priests and attorneys an organization's official ombudspersons are usually required to grant confidentiality to all who come to them for seeking advice or for filing complaints. They might be trained in de-escalating hairy situations of power abuse by superiors in scenarios of dependency like yours. Usually, they will not take any action that you didn't agree to, unless they are required by law to do so (which isn't the case often) or when the situation requires escalation to stop severe harm (e.g., if others are in danger by someone's action).

The exact rules might differ from organization to organization, but it is neither rude nor is there any shame in asking the ombudsperson what rules apply to their role before even deciding whether to confide in them. So if you don't make public that you're going to see the ombudsperson, doing so should pose near-zero threat to you and your PhD project.

Having said that, I will definitely look into it

Please do. Even if your university does not have an official ombudsman or ombudswoman, there might be unofficially assigned persons of trust in the institutes fulfilling a similar role and playing by similar rules. (If there are, again, ask what the rules are before proceeding.)

Your university's website probably has more information on this. If it's a larger university (and by the type of research you do, it probably is) the website and that information is likely available in both, German and English.

You can also ask your head of department, head of institute, the university's headmaster or any other of your boss's bosses, who the ombudsperson responsible for you is. If you ask them, you can (and probably should) do so without mentioning that (and why) you want to see the ombudsperson.

If you have problems finding an ombudsperson

I did a web search myself and found there is an official German organization called "Ombudsman für die Wissenschaft" (ombudsman for science), appointed by the renowned association DFG (Deutsche Forschungsgemeinschaft e.V.). The organization's website seems to be entirely in German, but they do have an English inquiry form for reporting conflicts and suspected violations of "good science" rules / suspected scientific misconduct.

They seem to be more focused on "good science" rules and scientific misconduct investigations than on conflicts, but according to their own examples in these presentation slides, they do consider "Inadäquate Doktorandenbetreuung" (inadequate / unsatisfactory support / supervision of PhD students) a violation of those "good science" rules, not just plagiarism, made up data, skewed results etc.

They also publish a "Liste der Ombudspersonen an deutschen Hochschulen und Forschungseinrichtungen" (list of ombudspersons at German universities and research facilities). I'm not sure how up-to-date that list is, but the people on it are probably still around. If they aren't active ombudspersons any more, they can probably tell you who's in charge of their chair nowadays.

Whether you confide in a local ombudsperson at your university or send an inquiry to the "Ombudsman für die Wissenschaft" organization is up to you. The DFS's white paper that lead to founding "Ombudsman für die Wissenschaft" is explicit about this:

Hochschul- oder Institutsangehörige werden ihre Probleme in der Regel bevorzugt einer örtlich erreichbaren Instanz mit Kenntnis der lokalen Verhältnisse vortragen wollen. Sie sollen dazu aber selbstverständlich nicht verpflichtet sein, wenn sie es vorziehen, sich unmittelbar an den [...] überregionalen „Ombudsman“ zu wenden.

(My translation: University and institute members will usually prefer to bring their issues forward to a locally available entity with knowledge about the local circumstances. Of course, they shall not be required to do so if they prefer to address the [...] supraregional ombudsman directly.)

On the basis of the information you've given, I think you should look for a new supervisor as soon as possible. Regardless of whether you manage to adapt the focus of your work, your current supervisor does not sound like someone you want to work with.

I couldn't get anyone to teach me at the time, so the whole experience was pretty traumatic

No one should have to figure out how to humanely kill animals by trial and error.

he tells me quite bluntly - "this is what you are required to do as part of your PhD"

This is your project, and if you can find an alternative way of addressing the aims of the project then you are entitled to.

he's paying me every month (which he reminds me of, every month)

It sounds like he wants a technician, not a PhD student. Doing a PhD is not about unquestioningly doing the bidding of a supervisor.

Other answers have made good suggestions about how to make sure that you don't just have to throw away the progress that you have already made. But find another supervisor to continue your work under!

You are two years into a four-year PhD, or perhaps you have completed four years out of six. It may seem long, but it's still early in your academic career. It's not too late to quit and restart, and you might even be able to jumpstart into a new PhD position using the work you've already done.

That might be your best option. Stop your current PhD. Not abruptly, but accept you will have no more data, finish and submit publications in progress, and meanwhile search for a new supervisor/plan where you don't have to kill your conscience. Your papers exist, and you have a valid explanation for a possible gap.

Change while you still can.