Slaughtered animal

On `Eid Al-Adha, is there a different way of sacrificing without killing an animal?

Dear Sheikh, As-Salamu `Alaykum wa Rahamatu Allah wa Barakatu. In a slaughterhouse there is a mute butcher. We want to know how he can say the name of Allah over the animal he slaughters.

Asalamalaykom,I have been invited to go visit relatives who live in a western country other than the one I live in, it is not that easy to find halal butchers in this particular city in Australia, therefore they just buy their meats from the local butcher not being sure of the way the meat has been slaughtered or killed and not being sure if the people who killed the animal are "ahlul kitab" or not, they do not eat pork though of course. Is it ok for me to eat at their house when I am invited, I feel bad refusing an invitation such as this but what is the shariahs view?Gazzakumallah Khayr