find
does not support parameter substitutions, you need to pass ${1%.*}
to the shell. But fortunately, that's not very hard to do:
find "$TRANSCODEDIR" -type f -exec bash -c 'HandBrakeCLI -i "$1" -o "${1%.*}".mp4 -- preset="$PRESET";
rm "$1";
mv "${1%.*}".mp4 "/path/to/converted/folder"' _ {} \;
So just to clarify; the "top level" is find -exec bash -c '...' _ {} \;
and the Bash script inside the single quotes contains three commands, all of which operate on the same input file.