The lama often refers to the Great Wheel when he is talking about this world—the world of the everyday. According to Buddhist belief, every soul in creation is caught up in an endless cycle of repetition and rebirth. We all die and then return to the world over and over again, with no change, and the only way to free ourselves from this Great Wheel of existence is by letting go of attachment and desire, and by recognizing the impermanence of all things.
The lama's Great Wheel also has a visual side to it, since he sketches out the Tibetan Wheel of Life to educate the people he meets about Buddhist religious belief. This Wheel introduces the Buddhist hells as well as the concepts of karma and worldly attachment through symbolic illustration.
When the Russian grabs at the lama's painting of the Wheel and tears it through the middle, his carelessness provokes the lama's anger and desire for revenge. The Russian's ripping of the Wheel indicates his disrespect for, and misunderstanding of, the lama's religious belief. It is only Kim—the well-established English kid, as opposed to this upstart Russian agent—who really understands the lama's use of his drawing to teach people about Buddhism.
The tear also represents the damage that this whole trip into the Himalayas has done to the lama's true religious practice. He has let his pride get away from him, since he keeps bragging about how well he knows the mountains. He has misjudged his loyal Kim: when he sees Kim skillfully disguising E.23 as a Saddhu, he assumes that Kim is giving in to his arrogant desire to show off, and he scolds Kim for his use of magic charms to satisfy his ego. And obviously, the worst example of the lama's brief crisis in his religious belief is the killing rage he feels toward the Russian agents for raising a hand against him.
The tear in the lama's illustration of the Great Wheel is both the cause of their fight with the Russian agents and the symbolic result of the lama's personal struggles with sin in the later parts of the novel.