Double left click on the atoms you want to delete and then press delete key of your keyboard. Similarly double left click on the bonds and delete them.
"I think when displaying bonds Vesta by default searches for the atoms beyond the first cell increasing the number of atoms displayed. You can change that by going into edit>bonds and selecting each bond type and changing its boundary mode on top to "Do not search atoms beyond the boundary". That way you only display the atoms mentioned in your POSCAR file not those of the periodic images."