An older version of the rule did use cut, if you are interested in the logic, it pasted it below.
function cut_line_at_point_cutter(line_feature, point_geometry) {
var search = Extent(Buffer(point_geometry, .1, "meter"));
var geo = Geometry(line_feature);
var segment = Clip(geo, search)["paths"][0];
// Rotate logic - https://stackoverflow.com/questions/45701615/how-can-i-rotate-a-line-segment-around-its-center-by-90-degrees
// Start and end points of the line
var x1 = segment[0]['x']
var y1 = segment[0]['y']
var x2 = segment[-1]['x']
var y2 = segment[-1]['y']
//find the center
var cx = (x1 + x2) / 2;
var cy = (y1 + y2) / 2;
//move the line to center on the origin
x1 -= cx;
y1 -= cy;
x2 -= cx;
y2 -= cy;
//rotate both points
var xtemp = x1;
var ytemp = y1;
x1 = -ytemp;
y1 = xtemp;
xtemp = x2;
ytemp = y2;
x2 = -ytemp;
y2 = xtemp;
//move the center point back to where it was
x1 += cx;
y1 += cy;
x2 += cx;
y2 += cy;
var cutter = Polyline({
"paths": [
[
[x1, y1],
[x2, y2]
]
],
"spatialReference": {
"wkid": geo.spatialReference.wkid
}
});
var new_lines = Cut(line_feature, cutter);
var line_a = Dictionary(Text(new_lines[0]))
var line_b = Dictionary(Text(new_lines[1]))
line_a['paths'] = remove_vertex(line_a['paths'])
line_b['paths'] = remove_vertex(line_b['paths'])
return [Polyline(line_a), Polyline(line_b)]
}