Okay, I just watched the first 20 minutes and while I'm by no means a Sion expert, I can at least point out some stuff that your game would've been aloooot better without.
1-That towerdive at level 1 was really, really silly, there's no other way I can put it. Towerdiving at level 1 is asking for a horrible death, plus you even wasted flash to actualy dive. I suppose you didn't expect to come out alive, and getting first blood and then dying isnt worth it, much less if you give the enemy first blood instead, less even if you waste your summoner's spells just to fail it.
2-At some point, it seemed like you just forgot to turn your E on as you exploded your shield. Keep in mind that any last hits from you, from spells or otherwise, work with his E's passive. You might want to just leave it on forever after you have some survivability.
3-At several points your exhaust could've turned the tide of the fight and killed jax and/or Yi, but you didn't use it, and sometimes you used it when the kill was nearly guaranteed.
4-You facechecked the brush when Maokai didn't have a sappling on it. Considering you were fighting Jax and Yi, this is deadly 90% of the time. You really, really need to play safer with sion n early game. AP sion really needs his items before he does anything, your second or death happened because you overextended yourself autoattacking minions close to the enemy turret, were Jax ad Yi (two champions that can practicaly teleport to you if you're in range, while doing damage) would be safe to pounce on you. Even if you stunned one, the other would kill you, as you had less then half of your health left.
5-At one point you tried to gank jax and yi from behind since jax had baout 30% of his HP, without warning Maokai. While he should've at least looked at the map and rushed to help you, it wouldn't hurt to warn him beforehand. That was mostly Maokai's fault though, if he did charged in to help you, jax would be dead, or you wouldn't have died in vain, in the very least.
6-One of the biggest mistakes you and maokai made was not letting enemy minions push. Playing close to tower is alot better for champions like maokai and sion, since jax and yi are melee aggressive champions, and being at tower would deny them of XP and last hitting while stopping most of their harassment. You guys were keeping their minions at the enemy tower, giving them ALOT of free ground to jump on you and just stomp you to death. Be glad they didn't know what they were doing, or else they'd have stomped you right out of the early game.
Considering this, all I can say is that you really need to play safer during the early game. Jax and Yi are very aggressive carry champions, level 1 Maokai and Sion really don't have the power to go toe to toe with them and win realiably, as both champions need their items. Altough Jax and Yi are both weak during the early game, they still have a higher damage then both of you, and their champions spells were both tailored for a first blood (Yi had both exhaust and ignite). What you should/could have done working on last hitting minions on the early game while harassing them if needed/possible.
At one point Jax was level 4 while you were level 1, and he also had 4 kills and 1 death before the game hit the 15 minute mark. Considering how dangerous jax and yi can be if they get a good early game, this is really, really bad.
TL;DR play safer during early game, be aggressive when you can actualy kill them and get out alive. It wouldnt even take that long, all you needed was boots and sheen.