Reordering the picture slides in a Mosic carousel is as simple as dragging and dropping them where you want them placed.
1.) Go to the page containing the Mosaic page with a carousel. Make sure that "Dislay" and the "Mosaic Layout" is checked
2.) Select "Edit" from the menu
3.) Select on the Mosaic page the carousel to activate the options buttons that are found in the right corner of the carousel tile
4.) To select and move a picture slide (Left-Click and Hold) the mouse button and move the slide down or up to another slide position and release the left mouse button. 
5.) Once you have made your changes make sure to click "Save" at the bottom of the page.