Never Stop Asking Why
Of course, your alternatives vary by how often you mail, but the point is don't have just two options — all or none. Create intermediate steps in between, and find the right balance for each dissatisfied donor. Removing a donor from all mailings sort of solves the problem, but it creates a whole new one — a donor who never hears from you so he or she stops giving. That's like cutting off your head to stop a runny nose.
2. Why are we including this content in our newsletter? Do donors care about it? There are things that get into newsletters (more than other pieces, I think) that serve no other purpose than to make someone on staff happy. Yes, that's harsh — but I've seen it far too often. Worse, the person we are appeasing may have left long ago, but the wasted real estate on non-donor-centric copy lives forever.
If you can, ask your donors what they enjoy about your newsletter. What do they want to see more of? Less of? Then use that input to make your newsletter more focused on the donor and less about the organization. At a minimum, ask, "What is the goal of the newsletter?" Then question if each article helps accomplish that goal. (If the newsletter has many goals, that's another problem to address. A newsletter that has to do everything usually does nothing well, in my opinion.) Your bottom line will thank you when you seriously ask why in evaluating a newsletter.
3. Why do we mail and email as often/as infrequently as we do? The email schedule is often more thought out because it's a newer addition to most fundraising plans, but direct mail has often been around for years, even decades if your organization has existed that long. How often you mail may have been determined long before you automated your mailings, and the frequency depended on how often you could get volunteers in to hand-stuff the mailings! Or you may have mailed more frequently because you didn't have the ability to see what mailings were producing so you just mailed more to hopefully capture every opportunity.