There are two major sources of oxygen in the world: phytoplankton, and trees. In real life, a single aspen tree can grow into grove of enormous size.
Suppose this tree were slightly bit more successful, and colonised the majority of Europe, Asia, and Africa. This tree would be responsible for a large proportion of oxygen proportion in this world, taking over the formerly biodiverse forests. This singular tree might have extremely mild genetic variations over its entire 85 million square kilometre (33 square mile) span, and shares circulation over the same area.
After an extended drought in South America, followed by a few unfortunate thunderstorms, the Amazon Rainforest began to burn.
To make matters worse, this aspen grove, the Heart of the World (though more accurately, the Eastern Lung of the World) got a prion infection, leading to a spreading area of dead tissue.
With the Amazon Rainforest (the Western Lung of the World) aflame, and the Eastern Lung of the World dying from infection, the concentration of carbon dioxide in the atmosphere would increase, and the concentration of oxygen in the atmosphere would decrease. The Eastern Lung of the World can singlehandedly handle the oxygen requirements for the entire world when healthy, of course.
If the atmospheric concentration of carbon dioxide increases sufficiently, then two consequences are likely. First, the acidity of seawater will increased due to carbon dioxide dissolving into water and forming carbonic acid. Second, the mean temperature of the world will increase, leading to melting of polar ice caps.
Should this second effect be sufficiently severe, then trapped gasses in the ice caps will be released, possibly leading to a positive feedback loop. Further, sea levels will rise, destroying habitats near to the coast. This may cause the death of mangroves (which fill a different niche from aspens, so will likely have remained extent until this point), and the extinction of mangrove-adapted life.
The increase in seawater acidity will lead to mass die-offs of coral, removing the niches of many forms of aquatic life.
The reduction in concentration of atmospheric oxygen, and the increase in atmospheric carbon dioxide may lead to asphyxiation of larger land-dwelling life, larger insects, and some aquatic mammals. Since this also corresponds to lower concentration of oxygen in water, this may also suffocate much aquatic life.
Though not all life will perish (plankton, some plants, many arthropods, and most microorganisms will likely survive), this will constitute a mass extinction event.
The Heart/Eastern Lung of the World must move, so aspen trees don't exactly fit. However, we might loosen the definition slightly. The Heart of the World forms a symbiotic relationship with a species of animal, known as Dryads. These dryads are completely dependant on the Heart, which excretes a nutritious syrup from specialised trunks, from which the dryads feed.
The dryads, in order to protect themselves from predators, have evolved to look very similar to the tree trunks. Further, they are very protective of these trunks (damage near to a feeding trunk worsens the taste of the syrup, so the dryads do their best to protect all the trees).
The dryads also are influenced by the hormone content of the syrup; the composition of the syrup is in turn controlled by the complex interconnected root network (which behaves almost analogously to a brain).
Taken together, an outside observer would see "trees" come to life to protect the grove as a whole.
It is, of course, obvious that if the tree dies, the dryads will go extinct.
TL;DR: If a giant tree provides most of the oxygen in the world, then if it dies, runaway global warming causes a mass extinction event. The tree is actually two species: the producer which is actually much like a tree, and the symbiotic dryads, which protect and carry out the will of the Heart of the World. The dryads move, and appear to be the exact same thing as the Heart of the World.