How to add negative filter in network tab of Chrome DevTools?

Note sure you're talking about the Network tab or the Console tab: I'll answer about both cases.

Network tab

Similar to Google's search operators, you can use the minus sign to filter out stuff in the network view, see the examples below.

Here you have the start network list:

enter image description here

If you type -, you'll see a list of types that you can select to filter:

enter image description here

Note that at the same time the resource names are filtered to those containing the minus sign:

enter image description here

For example you can filter out the GET requests:

enter image description here :

If you instead type a word, it will exclude all resources containing that word:

enter image description here

At the moment (*) you can't use the minus search operator, but you can use regular expressions.

For example to exclude the word browser-sync I use ^((?!browser-sync).)*$.

enter image description here

(*) Chrome 44.0.2403.125