Completely Remove from spacific page

This depends on how you are adding a SideMenu button to the site.

Are you adding the button to a widget area? If so you can use a plugin like Widget Context to specify which pages the widget is shown (or not shown).

Are you adding a button to an existing menu? If so then to hide the button on a specific page you would use some CSS like …

.page .open_sidemenu {
display: none;
}

… replacing .page with your specific page body class.

Oliver