I would use the Underscore.js library that has a list of useful functions.

without_.without(array, *values)

Returns a copy of the array with all instances of the values removed.

_.without([1, 2, 1, 0, 3, 1, 4], 0, 1);
// => [2, 3, 4]

Example

var res = "deleteMe";

$scope.nodes = [
  {
    name: "Node-1-1"
  },
  {
    name: "Node-1-2"
  },
  {
    name: "deleteMe"
  }
];
    
$scope.newNodes = _.without($scope.nodes, _.findWhere($scope.nodes, {
  name: res
}));

See Demo in JSFiddle.

var evens = _.filter([1, 2, 3, 4, 5, 6], function(num){ return num % 2 == 0; });

// => [2, 4, 6]

Example

$scope.newNodes = _.filter($scope.nodes, function(node) {
  return !(node.name == res);
});

See Demo in Fiddle.