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:

header.main-header.layout-logo-menu .cart-dropdown {
    display: none;

Here's a guide: How to add custom CSS / PHP code or modify the theme code - Hair Beauty Theme

Step 3: 

You can also hide the shopping cart icon on lower resolutions (mobile view) - please go to Mega Menu > General Settings > VamTam Additions > Enable WooCommerce Cart in Mobile Header