How to create a second partition on an external disk and is it safe? I want to create a second a partition in my hard disk where one (about 900 GB) is used for Time Machine and another (100 GB) is used to store info like a thumb drive.

I don't want any existing data to be lost. I know someone who partitioned his hard drive and it is now spoiled and not repairable. I have important info in this hard drive and this is my only one.

For your info, I am using a retina MacBook Pro with Mavericks and want to repartition a WD My Passport for Mac hard disk.
Yes you can repartition without losing data. Using Disk Utility, perform a repair on your drive to make sure the drive is free of errors (even better, use Diskwarrior if you have a copy). Then unmount your drive but don't eject it. Select the drive in the left hand pane, then go to the Partition tab. On the Partition Layout section click on the "+" to create a new partition. Optionally you can specify the new partition size. When you're happy hit the Apply button and wait.

If you've absolutely critical data on the drive make sure you have a backup (which you should have anyway) but I've done this many times without an issue.