Try the following:
dpkg-checkbuilddeps 2>&1 | sed 's/dpkg-checkbuilddeps:\serror:\sUnmet build dependencies: //g' | sed 's/[\(][^)]*[\)] //g'
First of all, dpkg-checkbuilddeps prints out the error to stderr not stdout. So it needs to be redirected to stdout to use pipeline.
Here is how to Redirect stderr and stdout in Bash
You used the regex ([^)]*) on:
sed 's/([^)]*)//g'
But it should be:
sed 's/[\(][^)]*[\)] //g'