In the past, the only way Mangog has been defeated, was through the following:
1. Odin attempts to temporarily get rid of Mangog by separating and setting free the entire race of beings that Mangog was composed of.
Without the hate of the entire race fueling him, Mangog temporarily dissipates.
There is no battle between Odin and Mangog in this first appearance, however, it is stated constantly that Odin is unable to beat Mangog and Mangog, literally, cannot be beaten in battle.
2. In this appearance, the writer pushes the unbeatable nature of Mangog even further. It is stated every couple pages. Also, in this arc Odin is actually shown several times, seemingly terrified of Mangog. Odin himself states that he cannot beat Mangog again and again.
Two different statements are made by 2 different characters that Mangog is more than a Thousand Times more powerful than Thor. This is on panel.
Initially, as Mangog approaches Asgard, Odin rides out to greet him at the head of the Asgardian Army. At this time Odin is at full power. As they come upon Mangog, he literally grabs the earth and tosses it, along with the entire army and a bridge that they were crossing. The only one left alive is Odin and he is a cowering wreck.
As Mangog comes up to Odin, Odin announces that he cannot defeat Mangog, but cannot allow Mangog to gain the twilight sword and destroy the universe.
At this point Odin uses his power to shunt Asgard to a reality so far removed from the 616, it won't matter if Mangog takes the twilight sword or not, because it won't effect the mainstream universe.
After this happens, Mangog pummels a weakened Odin a couple times and is actually shown to be carrying around an unconscious Odin for many pages as if he were a rag doll, while Thor tries to save his father. Finally, Odin receives an amp from the waters of the Twilight Well, (which is a double of the well that Odin also receives power from) presumably doubling his power. When this happens Odin says that his power is extended like never before, and still all he can do is disconnect Mangog from his power source of hate and violence, which weakens Mangog and sends him running.
However, doing this, even with the amp, ends up killing Odin himself without killing Mangog.
Also, in this story, Mangog defeats a being known as Kartag the Keeper. Kartag is the protector of the second Twilight Well and is hinted at having powers similar to Odin, probably due to the well he protects being a double of the well Odin uses. He also defeats Thor in battle as Thor tries to gain the mystical waters.
Mangog is shown defeating Kartag with one strike.
3. Third appearance has Mangog in the guise of Odin, ruling over Asgard while Odin is away. Mangog is learning to use the power of praise and adoration this time, instead of hate and violence. Mangog now has this new power-source.
This time, the only way he is defeated is when the realm learns that he is not Odin and Mangog loses his connection with the power of praise and adoration. But, again, he was unbeatable until the disconnection from the power-source.
4. The defeat at the hands of Thor was suspect. After horribly punishing Thor, Mangog enters a period of weakness for some reason, at which point Thor is able to gain the upper hand. Mangog is shown on his knees, but never ko'd. Even after Thor fires the Godblast directly into Mangog's throat, he is never shown to be unconscious. He remains on his knees but moving.
This is when Thor strikes a last time, sending Mangog off of a cliff. He is shown to fall as his position changes. After he hits bottom, he is not shown again, but he is never shown to be knocked out. It is more of a bfr, because immediately, as soon as Mangog is falling, Thor takes off after Thanos.
And, that's the story.