In order to remove the shopping cart icon in the main menu, you can follow the steps below:

Step 1:
You can simply deactivate the WooCommerce plugin and the icon won't be visible anymore. Please go to Dashboard > Installed plugins:

Step 2:
In case you are going to use the shop functionality, then please add the code below to the Custom CSS area:
.fixed-header-box .cart-dropdown {
display: none;
}
You can also hide the shopping cart icon on lower resolutions (mobile view) by adding the custom CSS code below:
@media (max-width: 959px) { .responsive-layout header.main-header .logo-wrapper .mobile-logo-additions .vamtam-cart-dropdown-link { display: none !important; }}Here's a guide: http://support.vamtam.com/solution/categories/159995/folders/9759/articles/200025-how-to-add-custom-css-code-