Add enough pond dye and you will choke the light off that the milfoil needs to grow, add the dye at ice out while it is still dormant and laying flat on the bottom.

I had milfoil in my pond a few years ago, pond dye in the spring followed by gully washers that muddied up the water two years in a row and it now completely gone. No chemicals used, I kind of miss it but it was getting out of hand when I first tried the pond dye. The first year I used it conservatively and it kept the milfoil from growing deeper than 4ft which was ideal for my pond.

Keep in mind that your fish community developed over time in the presence of milfoil, its sudden departure will upset the balance in your pond. You may need to harvest some fish to get things back in balance. It's likely you could end up predator heavy and light on forage once your milfoil cover is gone. Young of the year and small forage fish will have a lot fewer places to hide.