Magento standard can merge js and css. There is no standard functionality to minify this file afterwards.
How can we do this?
If you are in Magento 1.x, i would ignore the merging for css and js files. That functionality breaks more things that it fixes. There is no built in minification for Magento 1.x, so you will have to find a site that does that process (there are about 1.5 million of them on the web) and copy the css into the minifier and save the file with the new minified code. There is a few more things that go into making this work right, which i can clarify if this is the case.
If you are using Magento 1.9, it comes packaged with the RWD theme which uses SASS baked in. In that case, you can just use compass to compile the SCSS files to a minifided version. This setting is set in the config.rb file, which is also where you set the inline comments and other compilation settings.
If you are using a 3rd party theme, all bets are off on what they used.
If you clearify the setup you have, might be able to fish out a better solution for your use case.
**If you are using magento 1.9 simple css not scss. you need to first try merge css and js form the mangeto backend defult feature. If anyware break layout or desiging you need to check one by one which file was affect when useing merge css and js. I hop it will help you.**