The unsung hero of Harry Potter, Professor Severus Snape was a triple agent. He became a double agent for one of the greatest wizards of all time, Professor Albus Dumbledore, and the Order, but had Voldemort convinced that he was the Dark Side's agent at Hogwarts School of Witchcraft and Wizardry. Snape was also a gifted Potions student, funny without trying, tart-tongued, and a man who worked in silence, and behind the scenes. He revered the Dark Arts and tried to secure the Defense Against the Dark Arts post at Hogwarts for several years. He waxed eloquent about the Dark Arts when he finally got to teach the subject in Chapter 9 of the sixth Harry Potter book.
Snape's journey from Spinner's End to the finest school of magic was full of trials. At Hogwarts, he was sorted into Slytherin while his best and only friend from Cokeworth, Lily Evans was sorted into Gryffindor. His experience with unrequited love turned him into a hard shell of a man, and he shut off his emotions. A dive into Snape's past reveals he secretly defected from Death Eaters when his master, the Dark Lord killed the love of his life, Lily during the First Wizarding War. While Snape continued to love Lily until the end of his life, she did not love him back the same way. They most certainly were friends, but the events that took place after their fifth-year Defense Against the Dark Arts OWLs exam changed it all. Simply put, Harry's father, James Potter stirred up a fight that ended Snape and Lily's friendship. Though Snape was caught unawares, he retailed by casting a hex on James that gashed the side of his face. Given that Snape liked to dabble in the Dark Arts and kept company with Avery and Mulciber, could it be that he used Sectumsempra on his foe?
Sectumsempra For Enemies
Invented by Severus Snape at Hogwarts, Sectumsempra is a Dark curse that lacerates the target, causing severe hemorrhaging. As shown in Harry Potter and the Half-Blood Prince, Harry ended up mortally wounding Draco Malfoy with the Sectumsempra hex in a duel that took place in the boys' bathroom. Harry was unaware of what the spell did, and he'd found it in Snape's personally-annotated copy of Advanced Potion-Making. Snape's timely intervention healed Draco's lacerations and towards the end of the movie, Harry found out the Half-Blood Prince was none other than the man who cast a counter-curse on Draco, i.e., Snape. Moreover, the label of the Sectumsempra spell "For Enemies" makes it clear that Snape created it with the intention of using it against his foes.
As for Snape's usage of the hex, it's widely questioned if he himself used it on his arch nemesis, and the rich and famous, James Potter. As laid down in Chapter 33 of Harry Potter and the Deathly Hallows, "The Prince's Tale," Snape and James' rivalry began the day they boarded the train to Hogwarts. Snape, Lily Evans, Sirius Black, and James got to talking about Hogwarts Houses. While Snape hoped that his best friend, Lily would make it to Slytherin, James hoped to be sorted into Gryffindor. With this, an argument broke between James and Sirius on one side and Snape on the other. Lily who sided with her friend thought it would be better to leave the compartment, and so they did. Snape and James' rivalry snowballed with each year and finally came to a head in the fifth year after lot took their Defense Against the Dark Arts Ordinary Wizarding Levels exam and strode off toward the lake.
Snape Hexed James
While Snape and Lily did have their disagreements over Dark Magic, and the former's friendship with Slytherins of bad repute, they still saw eye to eye. It was James whose actions caused the end of their friendship. As laid down in chapter 28 of Harry Potter and the Order of the Phoenix, Harry learns in the Pensieve memory that his father was a show-off and Snape's bully at Hogwarts. "Snape's Worst Memory" reveals that after the Marauders took their D.A.D.A. exam in the Great Hall, they took shelter under a beech tree. Harry saw Snape seated in the dense shadow of a clump of bushes, immersed in his paper when James approached him. Since Snape was disarmed with "Expelliarmus!" there was little could do except wait for James' jinxes to wear off.
When Lily Evans tried to get James to leave her friend alone, Snape found the perfect opportunity to inch toward his wand. He directed his wand at James and without naming the hex, The Order of the Phoenix says "...there was a flash of light and a gash appeared on the side of James's face, spattering his robes with blood." He retaliated by hoisting Snape into the air, exposing his graying underpants to the school. This went on for a while, but Snape's calling Lily and her kind, "filthy little Mudbloods" (a disparaging term for Muggle-borns) was a nail in the coffin. As vile as this fight was, the question remains whether Snape gashed James' face using Sectumsempra.
The short answer is no. While yes Snape did gash the side of James' face, Sectumsempra is a far deadlier curse. When Harry used the hex in The Half-Blood Prince, Draco collapsed onto the floor, and severely bleed through his face and chest. Chapter 24 of The Half-Blood Prince says Snape traced his wand over Draco's deep wounds, muttering a song-like incantation of the counter-curse/ healing spell, Vulnera Sanentur thrice to half-lift Draco into a standing position. "You need the hospital wing. There may be a certain amount of scarring, but if you take dittany immediately we might avoid even that. . . . Come. . . ." said Snape in the sixth Harry Potter book. Had Snape used Sectumsempra on James, the latter would have some scars left on his face, as injuries caused by Dark Magic aren't easily healed. Therefore, it's highly unlikely that Snape hexed James with his specialty - Sectumsempra.