Concept:The correct phrasal verb for interrupting a conversation is "cut in".
Explanation:To "cut in" means to interrupt someone while they are speaking.
For example: "Please do not cut in when your teacher is talking."
The other options do not fit this meaning:
"cut through" means to pass across or shorten a route.
"cut off" means to disconnect or separate.
"cut from" is not used as a phrasal verb for interrupting.
Therefore, the blank should be filled with "in".
Answer:A. in