You have a website http://master.com and want to have a subsite http://slave.com or http://slave.master.com which is same as main site but has own database data for certain components.

Subsite should be created as parked domain for master site in your hosting panel first.

Both master site and subsite will use same database tables and hence have same contents.

But MightySites allows you to separate preferred database tables for each site. You will be able to manage each site's components from own backend panel of each site. I.e. slave site can have own categories (note that categories for all components which use native Joomla com_categories are separated), own articles, own menus and own modules, own users etc.

All other contents are managed from backend of master site as usual.

Each site can use own template style and load own CSS file.

Installing/updating components and Joomla update are performed in master site. Separated extensions should be additionally updated in slave sites in order to update own database tables, manual tables update can be required.