It looks like your code is increasing the position of path.segments[1]
every frame. I believe what you want is to subtract a portion of the difference between the segment and mouse positions per frame.
Try this:
var path = new Path.Line((0,0), view.center);
path.strokeColor = "black";
var pos = new Point(0, 0);
function onMouseMove(event) {
pos = event.point;
}
function onFrame(event) {
path.segments[1].point += (pos - path.segments[1].point) / 10;
}