How to redirect a category to another link?

Simply go to catalog > URL rewrite management and choose "add rewrite" then choose your "custom" from dropdown.

In Request path section enter your category link (ex. if url is www.example.com/category then enter category only) and in Target path enter your target url (ex. if blog url is "www.example.com/blog" then just "blog")

Hope this helps.

Update 1

If you receive Request Path for Specified Store already exists. then you need to go to catalog > Url rewrite management and then edit that category by finding it in that grid page.

Update 2

If none of above work for your try to add redirect in your .htaccess file

Redirect 301 /category.html http://www.example.com/blog.html

Explanation

For each store magento needs unique identity for request path, so you cannot add another and by default magento disables category rewrites request path field. So .htaccess is the best option here unless you update it from database directly. And good thing with the .htaccess is you can simply remove it when you need it but if you directly edited your database then will need to edit it again when removing.

Go to catalog -> URL rewrite management, create "add url rewrite".

choose "custom" in "Create URL Rewrite:" field.

In Request path give your "News menu url".

In target path give your "blog url".

save changes.

If you get any error, find your request path in the grid.If it already exists try edit that one or delete that one.