In ES6 (or using es6-shim) you can use Array.prototype.findIndex along with Array.prototype.splice:

arr.splice(arr.findIndex(matchesEl), 1);

function matchesEl(el) {
    return el.value === '14' && el.label === '7';
}

Or if a copy of the array is ok (and available since ES5), Array.prototype.filter's the way to go:

var withoutEl = arr.filter(function (el) { return !matchesEl(el); });

Solution with Identity

If you have object identity not just object equality (i.e. you're trying to delete a specific object from the array, not just an object that contains the same data as an existing object) you can do this very simply with splice and indexOf:

a = {x:1}
b = {x:2}
arr = [a,b]

Say you want to remove b:

arr.splice(
  arr.indexOf(b), 1
);

Solution with Equality

The question makes it unclear whether we are dealing with identity or equality. If you have equality (two objects containing the same stuff, which look the same as each other, but are not actually the same object), you'll need a little comparison function, which we can pass to findIndex.

a = {x: 1};
b = {x: 2};
arr = [a, b];

Now we want to remove c, which is equal to, but not the same as a:

c = {x: 1}

index = arr.findIndex(
  (i) => i.x === c.x
)

if (index !== -1) {
  arr.splice(
    index, 1
  );
}    

Note that I'm passing an ES6 style lambda function here as the first parameter to findIndex.

Unless you have the luxury of only writing for evergreen browsers, you'll probably want to be using a transpiler like Babel to use this solution.

Solution with Immutability

If you care about immutability, and you want to return a new array, you can do it with filter:

a = {x: 1};
b = {x: 2};
arr = [a, b];

Let's keep everything that isn't a:

newArr = arr.filter((x) => x != a)

Try:

var ar = [{"value":"14","label":"7"},{"value":"14","label":"7"},{"value":"18","label":"7"}];

for(var i=0; i < ar.length; i++) {
   if(ar[i].value == "14" && ar[i].label == "7")
   {
      ar.splice(i,1);
   }
}

demo