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:

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

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

For example you can filter out the GET requests:

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

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).)*$.

(*) Chrome 44.0.2403.125

google-chrome networking filter console

It seems as though the feature you are asking about is not supported on chrome.

Which is tracking a feature request for the functionality that you mention.