How do I avoid dying?

At first I have to say, that for sure this is the purpose of higher difficulties: making it harder to farm because of more damage, leaving you with the need of more gear or better dodging (using more defensive skills).

But for sure there is a way how you can make this easier for you. From your question I interpret that you are going for straight toughness, which is an error that a lot of people do. Toughness is the stat telling you how long you can prolong before getting killed, BUT toughness doesn't take the regeneration of your life into account. Meaning if you are fighting for a longer time (for example elites) and do not have a significant amount of life reg without health globes spawning you will die, even with a high amount of toughness. This doesn't mean you should get Life Reg/Life per Hit on every item, but you should definetely consider getting this on a few items.

Also a very important point is, that Vitality and Life% are the most useless stats after a certain amount(dependent on difficulty Level). For example in Torment 1 you really don't need more than 200k HP, Armor and +Res are multiple times better, because it doesn't only make you harder to kill, it also makes your Regeneration multiple times better.

In the most cases you should aim for armor and +Res on items, or even Reforge it, this will most likely fix your issues with higher torments.

If you want deeper inside thoughts into Toughness, you can also watch Moldran's video about it!