In Appearance/Menus click on the Screen Options tab at the very top right. In the “Show advanced menu properties” area, check the box next to CSS Classes. Use the either “hide-mobile” or “show-mobile” in the menu class field. NOTE: The max-width is the default Divi tablet break point width. You can change this to your specific needs. Add the following CSS code to the Divi theme options area or your child theme style.css file.

/* show hide on mobile */
@media only screen and (max-width: 980px){  
    .hide-mobile {display: none!important;}
}
@media screen and (min-width: 979px) {
     .show-mobile {display: none!important;}
}