A bit more information would help.
Best guess as to time of day? Daylight hours or after dark?
Where were the birds....best guess? Still out and about? Ranging? In a run or coop?
If in a coop, any signs of entry?
Condition of the dead birds found....other than the one missing it's head......bites to the back of the neck or big bites like a dog would do? Strewn about.....or piled in a group.....partially buried or ??????
How many birds do you have left?
The prime suspects for multiple kills all at once are coons during the spring when teaching the kids to hunt.....weasels, minks or one of the cousins year round, and dogs. Each has it's own signature.....none sound quite like what you found.
Video evidence of bobcats making multiple kills has recently turned up, and in that video, the cat left with the birds and came back for more.