You can't do much about this, and the degree to which you respond should be tied to how "related" your site is with the ones where he's doing the maligning. I'm going to talk here about:
- when to respond at all versus letting it go
- how to respond, if you respond
- other things you can do (this may be the most important part)
When and where to do something
At one end of the spectrum, if the user is maligning your community on his personal blog or Facebook page or Twitter account, then (a) you can't do much about that and (b) you risk making things worse by trying to intervene.
Stack Exchange (mostly Stack Overflow, from what I've seen) gets this sometimes -- some user wanders in, totally misunderstands the site, has a bad experience, and starts ranting about it on his blog. Or even: a user actually sticks around for a while, later gets disgruntled, and, similarly, starts blogging about it. I've seen one SO "hate blog", even. But here's the thing: if you engage the user on his turf, you're just giving him more ammo. "Oh look, those bad people followed me here! They won't leave me alone! They're stalking me!" Never mind that it's nonsense; he put a blog post out there and enabled comments, so he shouldn't criticize you for commenting. But you're playing for him and his friends, not a neutral audience; it's stacked against you and unless he's super-popular, you're not going to get a lot of positive benefits (like new users) from the exchange. This is why you pretty much never see SE moderators or employees commenting on such sites. What's more satisfying: to defend your site from such ravings, or to quietly snicker while he rants and gets no response? Don't feed the trolls.
So that's one end of the spectrum. At the other end, suppose your problem user threw a fit on your unicorns subreddit and then went off to the new unicorn-breeding subreddit next door. If he starts maligning you there, well, that's "in the family", so to speak, one subreddit to another. Even though they're different sites they have more of a common community than your site and Ranty Guy's blog, so (a) you care more about those people and (b) you probably have more "moral right" to speak up. (And depending on the site's rules, (c) you might actually be able to get some official support if he's outright lying.)
There's lots of stuff in the middle, of course. If he starts ranting about your unicorn forum on the unicorn-lovers mailing list, or on rec.pets.horses (because rec.pets.unicorns didn't get approved and that's close enough for him), or in a chat room for fantasy fans, you should balance the utility to be gained against the hassle of engaging. You might decide that even though they're the farthest from your topic there are good prospective participants among the fantasy fans, while you might decide that a digest-style mailing list, even one called unicorn-lovers, isn't worth your trouble.
The other case to consider here is outright misrepresentation. You said in the question that he's "representing" your site. How is he doing that? Is he claiming to be a moderator or administrator (fraud)? Or is he simply asserting as truth things that are not true, like "unicorn-breeding is off-topic there" when it's not (misrepresenting or lying)?
How to respond
I'm taking it as a given that any responses will be within the rules of whatever sites or communities you're visiting. Just because that guy is a problem user doesn't mean that you want to be one.
So, assuming the site has a suitable venue for response, I suggest a short, factual, dispassionate statement. For example:
Actually, unicorn-breeding is on-topic on r/unicorns and we've had several questions already (link 1, link 2). Our page about what is on-topic for us is (here). We welcome new users at any time.
If the user is acting fraudulently, like if he claims to be (or have been) a moderator, you'll need something a little stronger, but still calm:
Actually, Ranty Guy has never been a moderator on our site. Our moderators are listed (here). (Or: Our moderators are A, B, and C.)
If he makes false claims about things that happened on the site -- for example, if he claims that he was suspended when he wasn't -- then I advise against getting sucked in. At most I'd say something like this:
Suspensions are rare and are only for serious rules violations. Our policy on this is (here).
Notice what you've done there in the eyes of attentive readers. If you're right and are following your policy, then either Ranty Guy is lying or he wasn't really suspended for asking whether unicorns crap rainbows like he says he was.
Other things you should do
Ok, that's a lot about dealing with the acute problem, the guy who's blathering all over IRC about your unicorn community. People like that might do some damage (for the same reasons that boycotts can work and corporations sometimes respond to people dissing them on Twitter), but in the grand scheme of things, your community is built through positive actions having nothing to do with occasional disgruntled users.
Most people who consider visiting your site won't have heard of Ranty Guy. They'll have heard of Google for sure, though, so what do they find when they go looking? Do your SEO homework, and make sure you've got attractive content. That user may be telling people you're horrible, but you can show them how awesome you are. And you can do a lot more to control the awesome than you'll ever be able to do about the rants, so focus on what you can do.
Promote your site in whatever ways make sense among unicorn enthusiasts. Have a positive message, have content they're interested in, and some of them will come. Some of those will tell their friends. A few of them will blog or tweet about you. (By the way, make that easy for them -- a "tweet this" link in the right place, or meaningful URLs, can make a difference.) I'm not going to attempt a treatise on marketing (not least because I'm not an expert on that), but marketing is a real thing, with some well-understood principles, and just about any reasonable marketing that you do will almost certainly mitigate against one ranty user who has 17 Twitter followers and 20 blog readers.
Companies and prominent people have been trying to "control the message" about themselves for a long time. It doesn't really work, or not fully anyway. You can control your message, and you can do your best to get accurate and interesting information out there, but you can't -- and, in my opinion, shouldn't try to -- completely shut down the opposition.