How to remove part of URl with .htaccess?

I'm going to guess you already have some rewrite rules in place for URLs like http://www.example.net/content/index/mission

You need to find these rules and add a new one which uses a similar structure but 'hard codes' the content/index parts, for example, suppose the existing one was

RewriteRule ^content/(.*)/(.*)$ /content.php?param1=$1&param2=$2 [L,qsa]

You'd want to make a new rule to pick up /mission and rewrite it in a similar way, but before the existing rule kicks in, e.g.

RewriteRule ^mission$ /content.php?param1=index&param2=mission [L,qsa]
RewriteRule ^content/(.*)/(.*)$ /content.php?param1=$1&param2=$2 [L,qsa]

These are just examples - it will really depend on what your existing rules are.

You would need the rewrite module of Apache: mod_rewrite.

Then do something like this:

RewriteEngine on 
RewriteRule ^content/index/(.*)$ $1

Here is the official documentation of mod_rewrite: click