Hi, welcome to LQ!
echo 'Abc [abc].mp3'|sed -r 's/^([^]+) \[.+\](\..*)$/\1\2/'
Search (and remember) for all characters from beginning of line that aren't brackets:
Got space and something enclosed in brackets?
Find & remember everything from the dot to the end of line:
Replace the whole line with the two remembered bits:
P.S.: sed or regex makes little sense, in sed you commonly heavily rely on regex.