I'm not certain that your older hen did this...they don't typically "cut" a chick's neck...and the "hole" on the side of the butt doesn't look hen pecked either...could you possibly have a rat/mouse or cat that could have gotten chicks?
I agree with @jvls1942 hens peck heads, right at the brain...
Sal's Ole Timey Feed and Seed is in Columbia and is offering a lot of sexed chicks this year, ive never bought from them...but was told they have good quality. Carolina Rare Chicks in Lamar is run by world renowned Daniel Valasquez...he breeds show quality orpingtons and typically has marans...
I just got a silkie chick yesterday. The lady noticied it limped and so found out it only had 4 toes and gave it to me. Well after checking over the chick i found a hard bump on the bottom of one of the toes. It feels calcified...and seems to cause discomfort and/or pain since the chick limps...
I got this chick for my birthday, from a friend, as a sexed pullet...now im wondering if that is true...please help! Lol. Hatch date was 3/26, so chick is 8 weeks old.