Let's assume you have a file (allURLS.txt) with one URL per line. And you want to remove the http:// and https:// and store the result on the file cleanedUrls.txt
Here a very easy way:
grep "http:" allURLS.txt | cut -b 1-7 --complement >> cleanedUrls.txt
grep "https:" allURLS.txt | cut -b 1-8 --complement > cleanedUrls.txt
cut -b does a substring between i-j, with the option complement you select "everything else"