Evading and escaping the Reaper
One way is to use a seaglider to quickly get out of harms way. Another way is using a stasis rifle if you have one, this will cause it to stop for a while depending on how long you charged the shot. Finally the last way, that I can think of, is to find a cave where it couldn't go inside and hide.
If you don't have a seamoth then it is best to stay away from where they spawn. listen out for the noises they make and promptly swim away.
When you are in open waters, swim up.
Reapers won't chase you when you are near the surface.
When you are too far down to do that:
hide in a nook and hope it leaves before you run out of oxygen.
As mentioned in the answer by Mage Xy, Reaper Leviathans have good speed but they can't turn very fast. When you dodge their charge by moving sideways or up, it will zoom right past you and will need some time to turn around. You can use that time to escape.
As already mentioned in the answer by Mark Norman, hitting them with a good load from your statis rifle can give you enough time to escape.
You can deploy a creature decoy, if you have one with you (but you likely don't because they take up so much inventory space).
Reaper Leviathans are one of the the most dangerous threats in the game, and in my opinion it's the most terrifying (that roar gives me terror-chills just thinking about it). One of the biggest reasons they're so scary is because you can't outrun it with just a Seaglide - they move faster than you can.
However, despite their speed, they do have one limitation: they are not quite as mobile as you are. If you time it right, you can dodge their charge by turning sharply to the side before they hit you. Just like Sandsharks, they won't be able to turn fast enough to grab you. (This only works effectively if you're using a Seaglide - if you wandered into Reaper territory without one, you're fish food.)
As the other answer mentioned, there are several other ways you can deal with them as well, but the overall best way is to simply stay away from them. Other than the front entrance of the Aurora (which, contrary to popular belief, is usually Reaper-free), there is no reason to go into the biomes they typically inhabit. Every blueprint can be scanned in Reaper-less biomes.