Is throwing the Jmarat al-Aqabah al-Kubra, then a man clipping a single hair from each side of the pilgrim’s hair, correct, or does it necessitate a compensatory sacrifice (dam)? And what about past years?

Your question has two parts:

The first: The ruling on a pilgrim shaving or shortening his own hair, or that of another who wishes to exit the state of ihram, is permissible according to the majority of jurists, and this is the most preponderant opinion.

The second: The manner of exiting ihram, according to the guidance of the Prophet (peace be upon him) and his Companions, is for the one exiting ihram to take from all of his hair or to shave it all. This is obligatory according to the majority of jurists, contrary to those who say that a quarter of the head or three hairs suffice.

The most preponderant opinion is the first one (to encompass the entire head with shaving or shortening), based on the Almighty’s saying: "with your heads shaved and hair shortened," and based on the action of the Prophet (peace be upon him). Whoever does not do so must offer a compensatory sacrifice (dam).