You need to run yum as root, or with sudo (assuming you have sudo privileges). Since you are using yum, I assume you are either running a Red Hat or SuSe distribution? The openssl package is a standard module in the "security" distribution. FWIW, WHY do you want to remove openssl? It is a dependency for many other packages, so removing it could seriously impact your system.
If you are using SuSE, try using yast from the root user, as in:
When you try to uninstall openssl, this will give a much clearer picture of what you are trying to do. Since the programs that depend on openssl are multitudinous, you will have to declare that you are willing to 'break' many programs. Once you have uninstalled openssl and exited yast, re-enter yast and install openssl from a SuSE repository. This should fix all the broken applications that depend on openssl.