Kinds of People that we Meet at Work... and How to handle With Them

I believe it's always professional to stand up for yourself and ask for respect, as long as you demonstrate respect when making that request. 

If they say, "Nyah nyah nyah nyah nyah you are a silly-head. We don't have to listen to you," you do not respond using chants or words like "nyah nyah." You do not point out that their taunt is juvenile and would be more effective and memorable if they made it rhyme. The third graders used to tell me "Pencil geek, pencil geek, you're a dork and you are weak." I still remember this valuable lesson in how memory works. My therapist and I are working on it.

Before we go any further, I must give you a warning. In theory, your company is full of people committed to your mutual success. Your boss is a reasonable person committed to helping people grow and develop. And the culture at your organization is one of shared achievement. But if the reality is that the snarky person has blackmail on your boss (or if they're  romantically involved), or if your company is just a hotbed of politics driven by greed and petty power games, then all bets are off. Tattoo "Welcome" on your forehead and enjoy doormat status.

How to Deal With Difficult People? First, Build a Safety Net

Mature people address conflicts head on. Unfortunately, your snarker has already shown that maturity isn't high on the list. Start by waiting. Treat your snarker nicely, with respect. Maybe the problem will go away. That sounds passive, but it isn't. Because while you're waiting, you're calling everyone in your address book, chatting happily about all the exciting things you're doing on your job. You're sharing your thoughts about your industry, and trends, and the future. You're asking them what they're working on, you're offering them thoughtful ideas... so when you call them in two months looking for a new job, your relationship will be strong and they'll be willing to help. That is called "building a safety net." In today's grand world of layoffs-as-standard-practice, it's an absolute must.