A few years ago, the $28 billion business, headed by veteran Vyomesh Joshi, was the goose that kept laying golden eggs. It supplied most of the company’s profit while the PC group lost money and the corporate technology group struggled. Now new leadership and smart acquisitions have fixed the PC and corporate businesses, and printer sales are showing signs of weakness.

Though the printers and ink have so far pulled in a healthy $2.4 billion in profit this year for HP , the growth rate is slowing. To cut costs, Joshi last week announced a reorganization that trims the printer group from five divisions to three. The consumer hardware and ink businesses will be collapsed into one unit, laser printers and other enterprise operations will be collapsed into another, and graphics will be the last.

But while HP’s printing shakeup may keep profits healthy for now, it won’t bring new money in the door. The only quick way to do that would be to reverse a troublesome trend: Consumers, who make up the bulk of HP printer sales, are no longer bingeing on ink. HP had hoped that its advances in its printer technology would inspire more folks to avoid professional photo finishers, but that hasn’t really happened. And since HP is already the biggest company in inkjet printers, it can’t grow much by simply stealing customers from rivals.

In a twisted way, HP brought this on itself. A big part of the reason why the printing group is seen as troubled now is that investors have high expectations after it delivered reliable sales growth for so many years. Especially in the last decade, as home PCs became as common as televisions, HP played a big role in establishing the printer as a must-have accessory for producing everyday fare like book reports, letters and photos. Now it’s easy to see that printing isn’t as necessary to the PC experience as it used to be, with online social networks like Facebook and MySpace based largely on sharing information electronically, not printing it. But as printing sales growth slows, investors still expect the division to make up for it somehow.

For growth, HP is looking to markets like large businesses and commercial print shops, where rivals like Xerox have more experience. (See HP’s printer challenge.) The good news about those: they print a lot. The bad news: it won’t be as easy for HP to turn big profits. So to fund those efforts, HP is mercilessly cutting costs from its older, slower-growth printer businesses. Joshi has already jettisoned the digital camera business and outsourced much of manufacturing for black and white laser printers, and he’s still looking for more cost savings.

All of which makes sense – but is HP cutting too much, too fast? Under CEO Mark Hurd, the business groups have adopted a disciplined approach to innovation where each group funds tomorrow’s hit by cutting costs out of yesterday’s – a tactic few investors would argue with. But the downside is, innovation can’t be plugged into a spreadsheet, or put on a schedule. Just look at Apple’s computer business – it achieved only anemic growth for years, until a boost from the iPod, retail stores, and a switch to Intel chips recently put the shine back on the brand, but Apple continued to invest in it.

So far, analysts say there’s no indication that HP is slicing too far. Which is good – because I’ve heard you want to be careful with a golden goose.