In core JavaScript, you can remove a specific value from an array using the following approach:

Array.prototype.remove = function(value) {
var index = this.indexOf(value);
if (index !== -1) {
this.splice(index, 1);
}
};

var array = [1, 2, 3, 4, 5];
array.remove(3);
console.log(array); // [1, 2, 4, 5]

In the code snippet provided above, a new method `remove` is added to the `Array.prototype` to remove a specific value from the array. The method first finds the index of the value in the array using `indexOf`, and if the value is found (i.e., index is not -1), it removes that element using `splice`.

You can now use the `remove` method on any array to remove a specific value from it.