Inexperienced with Mesmer. Any advice for enemy groups in PvE?

So, I love Mesmer... On paper. It has an excellent assortment of tools and tricks, and I'd quite like to have those at my disposal. Problem is, my attempts to play it have typically left me frustrated and bored; it just takes too long to deal with groups of enemies with any sort of regularity. Taking on one group doesn't hurt too much, using Temporal Curtain to drag them all in for Sword 2, but then I'm dropped to a snail's pace for dealing damage while the cooldowns tick away.

How do you more experienced Mesmers handle this? Are Shatters the key? Is there a particular Phantasm that gets the job done? Or is it simply an inescapable fact that Mesmers are too busy playing mind games to actually hit things?

Its mostly Shatters, yes. Weapon skills that spawn clones (like Scepter 1) and the Dueling -> Deceptive Evasion trait, allows a constant stream of clones. Especially Chronomancers, who also have wells. An alternative, though, is to just spam Mantra of Pain a ton since its cool down is 1 second.

Staff auto-attack basically is a (bouncing) aoe-attack, also staff clones use it. When using a staff, hit one of the group to aggro them all, do not concentrate all your illusions on one mob only but tab through them and summon one illusion on one mob only. Then circle around to get the same effect temporal curtain would do and lay down Chaos Storm. Swap to Sword and finish them with Sw2. Weapon swapping is the key if you don't want to use the shatter skills.

Shatters are key for taking down groups in the open world, I think. They provide good AoE burst damage to complement your Blurred Frenzy cleave damage.

I think greatsword is also a pretty good open world weapon. The Phantasmal Berserker does an AoE attack that also cripples enemies, which can help you get some distance if you need it, and it has a knockback for the same purpose.

Also, don't be afraid to shatter for reasons other than damage. Distortion, the F4 shatter, is an extremely powerful defensive tool if you're feeling overwhelmed.