You can uninstall Structure from Plugin Manager the same way you uninstall other plugins. You can also manually remove structure JAR from plugins/installed-plugins directory when JIRA is not running.
When you uninstall Structure plugin, Structure data is not removed. It remains in place in structure sub-directory under JIRA home. (See Structure Files Location.)
After you have uninstalled Structure, you can completely delete its data by removing structure sub-directory. (We advise to at least create a backup copy though.)
Structure License is not kept in the Structure database, but in the main JIRA database. If you'd like to remove Structure license, you need to open Administration | Structure | License Details menu and use Uninstall License from that page – before you uninstall the plugin. |
It is perfectly safe to uninstall Structure plugin, then install it back again. (This happens, for example, when you upgrade to a newer version.)
All Structure data will be there unless you manually remove it.