Gee, I don't know -- is beheading a HATE CRIME?
Only if the peace loving jihadis, whilst reluctantly taking this last desperate measure to save their misguided victim's soul from God for Satan, use "hate language" directed at the victim's race, color, national origin, creed, religion, gender, sexual orientation.
Otherwise, it is is just "ordinary" murder.
goresalooza (Nurses Rock!) ...and Islamists stone!