OK, since my original answer was apparently too "technical" here's an adjustment: No you should not ask to have your manager removed from a distribution list that is for your whole department. It's just fishy-sounding. If you are trying to send emails to smaller groups, have your IT Team create additional groups that include people you want but not the manager, OR do the following if it is possible in your situation: (warning - mildly user-level technical answer follows)
I don't know if you're using Outlook for your email client or what, but I know that in Outlook you can manually expand your distribution lists and trim out the people you don't want to send emails to. We do that at my company all the time for things like birthday-card-signing invitations and things of that nature that should be a surprise or otherwise don't directly involve the extracted individual.
I would hope whatever email client you're using has a similar feature.
Also, if you're saying things to people that could be construed by the manager as a complaint, common courtesy should probably dictate that you take it up with the person "off-line" and not in a group setting anyway. I know I personally hate it when some jerk drops a dime on me in front of a group of people for no particular reason. However, if it's a group discussion about the best way to generate whatever reports, then merely saying "Hey, I realize this wasn't in the original requirements for this report, but it would be nice if we had x, y and z in it, too" really shouldn't upset anybody who's not a complete sociopath.
There are really a number of different ways to handle this situation. Heck, you could even try setting up a meeting with the manager where you explain that every bit of constructive criticism isn't necessarily damning towards the person in question and that having the ability to debate a little bit via the email system is a good thing and will help overall communication and productivity.