Certainly, it is arguable that Basil's murder is the ultimate act of insanity that Dorian Gray leads. It is after the murder of Basil that things just continue to go steadily from bad to worse in Dorian's life and where his inner demons just continue to take over in a most disparate way. Perhaps it is not even an accident that Wilde chooses Chapter 13 as the prime chapter to expose this climactic event in Dorian's life. We know Wilde was a person who gave importance to superstitions such as the number 13.
The murder happens in a very surprising manner. After all, Dorian does not plan to kill Basil: It is Basil who visits Dorian at very odd hours of the night prior to taking the midnight train to Paris. It is Basil who instigates the anger of Dorian by bringing up his bad behavior and the way in which Dorian has conducted himself during the years. It is also Basil who takes it upon himself to judge and criticize Dorian and in testing Dorian's patience in listening to things that he does not like to discuss, such as his choice of behavior.
When Basil does this, he is literally precluding his own murder. At this point in time, years have passed and Dorian is a completely different person than what Basil remembers. By now. Dorian has yielded to every single temptation of life, has led a life of debauchery and cares not what the people or society think of him. To add to his crazy life, he notices how the picture has mysteriously adopted every sign of sin and ugliness in its profile, showing Dorian the state of his own soul. This has been eating Dorian up for a while. Having Basil, who painted the portrait, coming to call him on his bad behavior is the moment when Dorian literally loses it.
Hence, when Dorian invites Basil to look at his own painting, complete with its signs of sin and evil, he is actually sort of blaming Basil for what is happening. After all, not long before Basil confesses to Dorian that he had put "too much of himself" in that painting.
Dorian Gray glanced at the picture, and suddenly an uncontrollable feeling of hatred for Basil Hallward came over him, as though it had been suggested to him by the image on the canvas, whispered into his ear by those grinning lips. The mad passions of a hunted animal stirred within him, and he loathed the man who was seated at the table, more than in his whole life he had ever loathed anything.
These lines clearly show us that Dorian is seized with a primal anger that is a result of the combination of the loss of his physical and spiritual control. He blames Basil, in a way, for painting the picture. However, it is Dorian who summons upon it his wish of never to lose his youth.
The evidence of his anger shows in the way in which he commits the crime. It is not intended. It is not planned. It is another sign of his instincts acting by themselves. Therefore it is clear that certainly the death of Basil is shown by Wilde as Dorian's ultimate act of despair.
Hallward stirred in his chair as if he was going to rise. He rushed at him, and dug the knife into the great vein that is behind the ear, crushing the man's head down on the table, and stabbing again and again.