"But what happened, Harry? I jus' saw them Death Eaters runnin' down from the castle, but what the ruddy hell was Snape doin' with 'em? Where's he gone - was he chasin' them?"
-- Hagrid (HBP28)
After an encounter with Harry during which Snape admits he was the Half-Blood Prince and shouts that Harry should not call him a coward, Buckbeak the hippogriff attacks Snape and chases him back towards the Hogwarts gates. Snape, along with several other Death Eaters including the Carrows, Thorfinn Rowle and Draco Malfoy, make it past the school boundaries where they disapparate.
Harry stumbles towards Hagrid’s burning Hut and tells him that Snape killed Dumbledore, which Hagrid can’t quite believe at first (HBP28).
The date of Dumbledore's death, which happens moments before this event, is given as June 30, 1997, on Pottermore.