I use the bulk rope and fill the spool up with all I can get on, get some tension on the spring and stick the rope end out the hole and clamp the rope so it doesn't go back in.
Then I thread the handle on the rope and pull out enough for good spring tension - tie the knot in the rope and pot the stater back on the saw. You have to pull out on the handle and jiggle a little to get the starter to seat.
There are different thicknesses of starter rope.
There may be something inside your starter that is cutting the cord?
If the cord gets over the edge of the pulley, it is sure to chafe and break.