Well, this does seem curious:

$ perl -v
This is perl, v5.6.1 built for i586-linux
...
$ perl -e '$u="http://www.domain.com/hi.html?a=b&c=d";
 print $u,$/;
 $u=~s/(.*?)\?(.*?)/$1/gs;
 print $u,$/;'
[download]

produces:

http://www.domain.com/hi.html?a=b&c=d
http://www.domain.com/hi.htmla=b&c=d
[download]

But you said that you only wanted the first part (before the "?"), so why did you put parens around the second part? It does work as desired this way:

$ perl -e '$u="http://www.domain.com/hi.html?a=b&c=d";
 print $u,$/;
 $u=~s/(.*?)\?.*/$1/;
 print $u,$/;'

http://www.domain.com/hi.html?a=b&c=d
http://www.domain.com/hi.html
[download]

For that matter, whether or not you use the following part as well, why not split:

$ perl -e '$u="http://www.domain.com/hi.html?a=b&c=d";
 print $u,$/;
 ($ub,$ue)=split(/\?/,$u,2);
 print "$ub :: $ue",$/;'

http://www.domain.com/hi.html?a=b&c=d
http://www.domain.com/hi.html :: a=b&c=d
[download]

Still, the initial example is baffling, and I hope someone can explain why it should behave the way it did, just for our communal peace of mind. The final "gs" is of course superfluous for this example -- the behavior is the same with or without those qualifiers on the regex. (And "extra strength" is not really an appropriate reason for using them, anyway; check their descriptions in perlre to see what their proper, intended functions are.)