When starting an exclamative sentence addressed to someone, espèce de is colloquial and always derogatory unless if teasing/deuxième degré ("tongue in cheek"?) :

Espèce d’abruti !

In other cases, espèce de might just mean a specie of sth without negative connotation:

Le chimpanzé est une espèce de primates.

Il y a là une espèce de miracle qui ressemble à celui de l’amour.

Note the plural to primates, because primate is not an abstract concept but a collection of known species.

See also: « Un espèce de » ou « une espèce de » ?

“Espèce de” can be used the same way you use “kind of”. It’s actually the literal translation.

So in an insult, you would say “Espèce de crétin” which translates to “Kind of dumbass”, meaning “You’re part of the dumbass species”.

But you could use it in two other contexts: if you’re really reffering to “a part of that race”, as in jiliagre’s answer, “une espèce de primate”, or if you want to bring the same nuance as “It’s kind of a street gang” : “C’est une espèce de gang de rue”, “.. une sorte de…” .

Some examples of positive uses of “Espèce de…”

It could be teasing rather than insulting while addressing people we like/love/appreciate:

To a kid who just played a cunning practical joke:

• Espèce de petit garnement / sacripant !
• Espèce de petite fripouille !

Positive or neutral, showing respect to some extent at least: To someone who just spent ten minutes exposing some freakishly out-of-this-world maths to people who are not into that so much:

• Mon espèce de givré des chiffres, toi !

_{Or as the previous would likely be heard in Quebec:}

• Mon espèce de capoté des chiffres, toi !

It could also be used as an antiphrasis, as a way to express thankfulness, surprise (usually, we’ll be using Mon espèce de):

To a friend who just showed up with an unexpected and large gift:

• Mon espèce de fou, toi !

Between lovers, as a false insult and a real way of showing true appreciation:

Espèce de coquin(e) !

Another case that I did use at some point in reality, when a fox showed some interest in what I was doing and kept exploring around what I was laying out:

Espèce de petite bête curieuse, toi !

It’s been noted in a comment here below that all the propositions I made were ironically using insults, and that from this standpoint, any bad word or expression could be used this way.

I believe otherwise. All the so-called insults I presented are either benign (coquin, bête curieuse) or mitigated (PETITE fripouille, givré DES CHIFFRES, i.e. from an academic matter), and a harder insult would be rude and aggressive, no matter how much irony or antiphrasis you put into it (Espèce d’écrivaillon; Espèce de vieux schnock; Espèce de gros niaiseux).

Also, there is no such thing as “Espèce de généreux donnateur !” used as a thanks to a philantrope or a volunteer. It is just not part of the habits or usage of French at any level.

Furthermore, I would even go as far as to say that when a compliment is used following “Espèce de…”, it is actually also ironic, and it carries a bit of reproach along with the compliment: a husband who would say “Mon espèce de sauveuse de l’humanité” to his wife would either:

• acknowledge the hard work she’s putting into whatever she does to help people, but also hint that he doesn’t see enough of her;

… or, in other circumstances…

• point out that despite her great views and values, her work might not be as effective as she thinks or would hope (for whatever reason: humanity doesn’t want it, or others do it better, or more money would be required to make things more efficient, …).

The phrase “espèce de …” does not necessarily carry a negative connotation. You can say, for instance:

J’admire cette espèce d’assurance glaciale chez lui.

As you can guess from the verb “admirer”, there is nothing even remotely negative about the phrase here. On the other hand, if you have such an insult in mind:

Ne venez pas me bassiner avec des histoires sans aucune espèce d’importance !

Or if you’d prefer something neutral:

Elle était habillée d’une espèce de robe noire semblable à la tienne.

"espèce de X" can also be used to talk vaguely about a thing.
This would be similar to "thingy" or "sort of" in English:

« La¹ Gameboy, c’est une espèce de truc électronique ».

“The Gameboy is an electronic thingy.”

¹: Oui je sais, c’est « le », mais je refuse de l’accepter…