Tukemuth is a level 73 non-hostile rare mammoth with approximately 40k health. He can be found patrolling all over the middle of Dragonblight to the west of Wintergarde Keep and east of Galakrond's Rest. I have indicated the area where he patrols in green on the map below. He is one of three rares located in this zone. The other two are Scarlet Highlord Daion and Crazed Indu'le Survivor.
Tukemuth is part of the Northern Exposure and Frostbitten achievements. He drops Mammoth-Riding Boots which are level 72 bind on equip cloth boots with a random enchant. Like other Northrend rares, he also drops Abandoned Adventurer's Satchel, which generally contains about 20 gold, a full stack of frostweave cloth, and often times a few crystallized elements. He also yields a decent amount of experience for leveling characters.
For me this was one of the hardest rares to find. I've found him dead once or twice but live Tukemuth was pretty much a myth to me for the longest time. I believe its mainly because of the area that he patrols. It's highly traveled and the area itself that he patrols is huge. You can't just fly over a little portion of it and decide hes not up, you really need to check out the whole thing.
When he is up though, you should be able to spot him from pretty far away as he is HUGE.
A note to characters finding him around his level: Take precautions, he hits pretty hard with his trample ability. 3k + per hit. He moves VERY slow though, so classes with dots can safely dot him up and kite him around.