Using an AppleScript to kill an AppleScript

Here is how I'd do it:

In Terminal:

kill $(ps ax | awk '/[C]onnect Screen Mirroring - Master Bedroom/{print $1}')

Using the do shell script command in AppleScript:

do shell script "kill $(ps ax | awk '/[C]onnect Screen Mirroring - Master Bedroom/{print $1}'); exit 0"

Using awk eliminates the need to pipe to grep twice while allowing it to return only the value of the first column of ps output, which is the PID, and by placing square braces around the first character [C] it isolates the output to the occurrence being looked for, not what's generated by the awk command itself.

Using command substitution, $(...), it returns only the PID to the kill command.