I haven't played that game, but I think you might be able to get started by using Sprite Effects. There is an example in the Construct 2\examples folder called 'Sprite effects.capx' that you could look at to get an idea of how these effects work, if you don't know already.
I was thinking that you could create a small circle sprite (or square) called "Ground" and set its effect to 'Destination In'. On the same layer, add your ground graphic to a sprite and call it "Ground Image". Make sure "Ground" is on TOP of "Ground Image".
Now, if you set it up correctly, the "Ground Image" will only display where you have "Ground" objects. What you can do to start is have "Ground Image" fill up the whole screen, then place "Ground" objects all over it. Have an event that destroys "Ground" objects if they are clicked on.
Now, when you run the game, it'll look like there's ground everywhere and as you click on different parts of the ground, they disappear. You can work up from there to get the effect you want. I think this is a good approach, because you can use the "Ground" objects to interact with your environment (such as by giving them a 'Solid' attribute), which will give the illusion of a real, dynamic surface.
Alternatively, you can use the Canvas object to draw the ground dynamically as rfisher suggested. This will give you better results, but will be harder to code.