HTML:

<ya-map ya-zoom="10" ya-center="[37.64,55.72]">
    <ya-geo-object ya-source="geoObjects[0]" ya-options="{strokeColor: '#00000088',strokeWidth: 4,editorMaxPoints: 6}" editor-menu-manager="editor" ya-edit></ya-geo-object>
</ya-map>
    

javascript:

$scope.geoObjects=[
    {
        geometry: {
            type: 'LineString',
            coordinates: [
                [37.50,55.80],
                [37.40,55.80],
                [37.50,55.70],
                [37.40,55.70]
            ]
        },
        properties: {
            balloonContent: "Ломаная линия"
        }
    }
];
$scope.editor = function (items) {
    items.push({
        title: "Удалить линию",
        onClick: function () {
            $scope.$apply(function(){
                $scope.geoObjects.length=0;
            });
        }
    });
    return items;
};