It depends how you want to select it, to remove by text:
$("select[name=ShippingMethod] option").filter(function() { return this.text == "Opt1"; }).remove();
Or the selected one:
$("select[name=ShippingMethod] option:selected").remove();
Or the second one:
$("select[name=ShippingMethod] option:eq(1)").remove();
Or the last one:
$("select[name=ShippingMethod] option:last").remove();
To just select option 2 by text, you can use the same .filter() approach above:
$("select[name=ShippingMethod] option").filter(function() { return this.text == "Opt2"; }).attr("selected", true);
You can test it here.