You must learn a special skill to tame Feathermanes. It is taught by a Tome of the Hybrid Beast. See our guide for the pre-requisite achievements.
Undead Taming
Forsaken hunters automatically know how to tame undead creatures. Hunters of other races must learn the skill from a Simple Tome of Bone-Binding which is a rare drop from miscellaneous Elite NPCs throughout Maldraxxus and its associated dungeons: Plaguefall and the Theater of Pain.
Found atop a plateau southeast of Obsidian Citadel (approximately 33,76). Currently, you can only tame this undead gryphon while you're still levelling, or soon after reaching 70, as it relies on a quirk of level scaling, as there's an intended delay with NPCs scaling to your new level. Advance your level to at least 62-63, so that the creatures of the Waking Shore are (temporarily) around two levels lower than you. Slurpo is normally set to scale 2 levels higher than the regular creatures, but the delay in level increase means that it should actually appear at your level. Some time after you reach 70, it will scale up to 72 and remain untameable until the next expansion.
Level scaling: Most NPCs will scale with the Hunter's level, within the constraints of their level range. Hunters can tame regular NPCs up to 2 levels higher than them, but can only tame elite NPCs of the hunter's level or below.