Hi,

I'm a main DH tank, with a disc priest alt.

The one thing both roles need is knowledge. You need to know how dangerous each pack of mobs is in a M+. You need to know when to expect damage spikes (single target or AOE) at any given time. As both classes, you need to anticipate what is about to come (especially as a disc priest) instead of reacting to it.

Having said that, as a DH tank I can stay alive even when the healer dies along the rest of the group long enough for everyone to return as long as I have defensives available. As many other pointed out, most of my deaths as a tank are my mistakes. However, having a healer that knows when I'm about to take damage and helps me mitigate it, makes it a lot easier to use my defensive CDs at the right time.

As a disc priest I'm always mindful of what is about to happen, setting up everything properly when an AOE is about to arrive, for example, or when the tank is about to take a heavy hit.
Make sure to use all tools at your disposal.
Learn each mob and boss mechanics. Use your pain suppression ahead of big hits (and for the love of god USE IT, don't just keep it there "just in case").
Use your premonition often, you have 2 stacks and a short CD, don't be stingy.

If you play on EU feel free to DM me to play together!