In big cities people are cut…….from nature.

The correct option is off.

Explanation:
In English grammar, a phrasal verb is formed by combining a verb with a preposition or adverb to create a specific meaning. In this sentence, we need to choose the preposition that correctly completes the phrasal verb starting with "cut".

Let's analyze the meaning of the phrasal verbs formed by the options:

1. Cut off: Means to isolate, disconnect, or separate someone or something from something else. The phrase "cut off from nature" perfectly conveys that people in big cities are isolated or disconnected from the natural environment.

2. Cut down: Means to reduce the amount or quantity of something (e.g., "cut down on sugar") or to fell something like a tree.

3. Cut away: Means to remove parts of something by cutting, often used in a physical context (e.g., cutting away dead branches).

4. Cut out: Means to remove by cutting around the edges, or to stop doing something (e.g., "cut out bad habits").

Therefore, the phrasal verb "cut off" is the most appropriate choice to express being isolated or detached from nature.

Complete Sentence:
"In big cities people are cut off from nature."