See javascript substring.
For your example use this:
var string = "I am a string";
console.log(string.substring(7));
OUTPUTS
string
UPDATE
For removing a portionof a string, you can do it by concating the first wanted characters with the last wanted characters, something like this:
var string = "I am a string";
console.log(string.substr(0, 5) + string.substr(7));
OUTPUTS
I am string
If you want to have a direct function for removing portions of strings, see Ken White's answer that uses substr instead of substring. The difference between substr and substring is in the second parameter, for substring is the index to stop and for substr the length to return. You can use something like this:
String.prototype.replaceAt = function(index, charcount) {
  return this.substr(0, index) + this.substr(index + charcount);
}
string.replaceAt(5, 2); // Outputs: "I am string"
Or if you want to use start and end like (7, 10), then have a function like this:
String.prototype.removeAt = function(start, end) {
  return this.substr(0, start) + this.substr(end);
}
string.removeAt(7, 10); // Outputs: "I am a ing"