DISCLAIMER: I don't own Superman, the Justice League or Asura's Wrath.
Superman flew above the Earth, looking for the one called Asura. Asura was a demigod who possessed impressive powers, including magic attacks that put Black Adam to shame, and strength comparable to that of Doomsday. Asura had defeated Captain Marvel several days past, and Superman intended to be Asura's next opponent, and his last.
He turned when he heard an explosion, and he knew straight away that Asura was fighting another member of the Justice League. Superman flew down to the ground at incredible speed.
Asura delivered a massive punch to Wonder Woman's face, knocking her out. He turned to see the one called Superman standing behind him. Superman flashed forward, punching Asura onto his back. Asura recovered fairly quickly, but Superman was upon him before he could stand, punching him repeatedly. Superman threw Asura back, blasting him with heat vision. Asura landed on his feet, Superman still blasting him with heat vision.
However, Asura was barely affected by the heat vision, as his tolerance to both heat and energy was massive. Asura threw a mantra attack at Superman, but Superman dived to the side, avoiding it. Asura's magic attacks could destroy Superman if they hit him, but Superman had no intention of being hit. Superman charged into Asura, picking him up by the neck. Asura's fists collided repeatedly with Superman, and they hurt Superman, but the fists each broke after several hits, until Asura had only one arm. Superman gripped Asura's head, squeezing it and attempting to crush it. Asura slammed his foot into Superman, launching him back.
Superman recovered in mid-air, flying back at Asura. Asura charged also, preparing his remaining fist for a final hit. Asura's fist slammed into Superman's face, shattering on impact, while Superman was launched back, smashing through several buildings. Superman returned almost immediately, attacking a now armless Asura. Asura slammed his foot into Superman's incoming fist, and the two engaged in a battle of strength. Asura forced Superman's hand back, but Superman jumped onto Asura, attempting to crush him. Asura slammed his forehead into Superman's, and the two once again struggled to push each other back. Asura started to glow red with mantra, and Superman jumped away, narrowly avoiding being vapourised by the blast Asura released. Asura jumped up, while Superman flew into him, punching him at lightning speed. Ignoring the punches landing on his face, Asura wrapped his legs around Superman, and released a blast of mantra.
Asura struggled to his feet, standing over the wounded, barely alive Superman. Superman's strength was returning, draining strength from the sun, but Asura did not allow him the time he needed. Asura slammed his foot on Superman's face, but Superman caught the foot in his hand, forcing Asura back. Superman blew at Asura with his super breath, but Asura released more mantra, and easily stood his ground. With a roar of rage, Asura released a blast of mantra which tore up the empty city block. The blast was visible in outer space, and was seen by Batman in the Watchtower.
Asura lifted his foot off the charred remains of Superman, turning his attention towards the sky, where the Watchtower was visible to his stronger eyesight.
Reasons for this outcome:
1. Asura is highly resilient against blunt force and energy attacks. His only vulnerability is blades, which Superman does not have. Heat vision is an energy attack, which Asura would certainly survive.
2. Mantra is a technological power source, but it comes originally from the god Chakravartin, and clearly possesses magical properties. While there is a slightly grey area as to whether or not mantra is magic, the evidence would suggest it was. Superman is vulnerable to magic.
3. Asura is clearly a better fighter than Superman, as he shows himself to be very capable in combat, albeit a bit straight forward in his thinking. Superman relies on his power, and his training is so clearly inferior. He was trained by Wonder Woman, who uses a predictable Greek fighting style, and also by Batman, which is clearly ridiculous. How do you effectively train someone who can throw you like a javelin?