If you use an ax, it must be very, very sharp. I did a duck first and it wasn't , took 3 blows, arrgh. Now I use a .22 pellet to the head to stun them first, then cut off head.Nicer way to go I think. Storeys guide to geese, suggest using the broomstick method, but I am older and it would be too hard. As far as 'family" . I have raised and sold them. Yes , they mourn for a bit, but a new girlfriend did the trick after I sold my first. I had one choke to death and the flock didn't seem to care . However , I have raised some and then separated and they do seem to know one another and greet. That said, as the books say, just kill out of sight of the others. I would stun the bird first, like Storeys Guide says (they use a stout stick and wack them on the head , much like I use a pellet gun to the head...knocking them unconsious first, then you could just cut jugular or head off to bleed out....Their necks are Very tough.