Hold on…”The Death of Time”? Nothing even remotely like that happens in this episode. This whole thing is a mess!
OK, so, what did happen was the Daleks built a time machine and have the ability to track the TARDIS through time and space. After Ian and Vicki get lost down a trap door with the device the Doctor uses to find the TARDIS, the Doctor and Barbara go to look for them and are stopped by the fish like people of the desert planet they are on, the Aridians. Sure, the Daleks have a couple to dig out the captured TARDIS, but the Daleks found a good way to avoid paying for their labor costs by killing the slaves.
As it is, the two that find Barbara and the Doctor are friendly and take them back to the remains of their underground city. What happened to those guys? Well, the planet used to be a lot more aquatic, but then a second sun appeared in the sky, drying up the seas and killing most of the native life except the Mire Beasts which took over the underground city.
What’s a Mire Beast? Oh, big tentacled thing. Looks like an octopus. You know the type. Made of rubber and all that. Oh, yeah, the Aridians are setting off explosions to trap the Mire Beasts in other parts of the city, and guess where Ian and Vicki are.
The good news there is Ian and Vicki get to safety before the blast. The bad news is Ian gets a bump to the head and decides to take a nap.
The further bad news is the Daleks told the Aridian council to turn over the time travelers or else. And it looks like the Aridians are going to do just that.
However, there is some good news. Vicki found a way out and even located the TARDIS. It’s being guarded by Daleks. When she goes back underground, she gets caught by the Aridians but they just take her to the Doctor and Barbara. When a Mire Beast bursts through a wall and starts to, I dunno, eat an Aridian, the time travelers take a powder back to the exit Vicki found. And Ian woke up and has a plan because of course Ian has a plan.
It mostly involves luring the one Dalek guarding the TARDIS away and dropping it down the tunnel, allowing the humans to escape in the TARDIS. That involves a lot of jumping up, saying something like “Yoo hoo!” and then ducking until the Dalek lumbers too close to the pit and falls in.
This actually works.
Anyhoo, the TARDIS disappears and the Daleks are off in pursuit of them wherever they go next.