Shingetsutan Tsukihime

The story follows Tohno Shiki, a teenage boy who, after a near-fatal accident in his childhood, gained the mysterious power to perceive lines covering everything around him. When he cuts along these lines, whatever it was immediately falls apart with a clean cut; in other words, killing it. He would have quickly gone insane from living in a world that could fall apart so easily, had it not been for a wandering self-proclaimed magician who gave him a pair of glasses that blocked his unnatural perception when worn. Soon afterwards, he was disinherited from his family and sent to live with some relatives. For eight years he lived a normal life, hiding his special eyes, until one day he receives a letter inviting him to come back home. Shiki suddenly becomes caught up in strange and life-threatening series of events, ones that are somehow linked to his childhood accident and a forgotten past... (Source: Mangamonster.net)