well, kinda late, but I have experience slaughering them (and almost all kind of ediable animals)
all that you need is just a sharp knive, and some sort of large bucket, and things go simple, you grab the rabbit, put it into the bucket, expose his throat, and slit it in the neck, as near as the head if possible. After that, hung it upside down and let the blood drains out, that way, you can done this in minimum mess (seriously this was most clean, doing it classic way in the bucket).
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