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In the Harry Potter universe, the notorious and forbidden set of spells known as the Unforgivable Curses is exclusively used by dark witches and wizards (with Snape's killing of Dumbledore the only notable exception.) Imperio enables the caster to control another living being while Crucio inflicts intense pain upon the recipient. The last and most egregious of the three, Avada Kedavra, kills anyone unfortunate enough to be in its path instantly.
Of all those known to have used the spell in the lore, Voldemort is perhaps the wizard who casts it most frequently. He uses the killing curse at least 20 times during the books alone and there are records of him using it all the time during the First Wizarding War, most notably on the Potters. So why, when it came time to kill his seemingly loyal follower Severus Snape, did he elect to avoid what seems a surefire way to end someone's life?
Voldemort Wanted To Gain True Control Over the Elder Wand
Snape finds himself in Voldemort's crosshairs as Harry Potter and the Deathly Hallows approaches its climax. The Dark Lord believes he needs to kill his old ally to achieve true control over the Elder Wand as part of his plan to become the master of Death. It later transpires that he is, in fact, wrong in this belief; Snape was never actually the true master of the most powerful wand in existence. Draco Malfoy was the one who had disarmed Dumbledore to become the rightful holder of the wand.
It is this misguided belief that motivates Voldemort to act as he does. The film differs from the book in its portrayal of the method used to kill Snape, but neither uses the killing curse for the simple reason that the Elder Wand is said not to be able to act in direct opposition to its master. As a result, the book has Voldemort command his snake Nagini to kill him, while in the film, a wordless spell slices the throat of Snape before Nagini goes on to strike him multiple times and finish the job.
Voldemort Wouldn't Have Killed Snape Unless Absolutely Necessary
Before the Dark Lord carries out the act, he says to Snape that he regrets having to do so. There could be several reasons for this, but it's important to remember the esteem that Voldemort held him in. Snape was one of the few Death Eaters Voldemort truly trusted and respected. He was a reliable servant for many years before the events of the Battle of Hogwarts. At some of Voldemort's most triumphal moments, Snape had been present, cementing his position by finally being the one to kill Albus Dumbledore.
Equally, Voldemort could have some regrets over the more brutal and bloody way he felt he had to kill him. The lack of dignity offered in death might even have affected someone as cold and calculating as Voldemort. When all is said and done, he is still losing who he perceives to be his most faithful servant, and it's a noticeable loss, even if it isn't an emotional one.
Control of the Elder Wand was an obsession for Voldemort ever since he reemerged during the events of the Goblet of Fire, and he wasn't prepared to take any chances. In the lead-up to the Battle of Hogwarts, he felt the wand did not work as well as it should have, and he would do anything to have it become the wand of legend that he was expecting. This unwillingness to take chances on the wand's loyalty led to Snape's unusual and savage death.