No, don't cut close to the property line...
Valid points are made, and I did take them into consideration. it will depend on how big the tree is already, how big the roots that you cut are and the proportion of roots you cut relative to the rest of the roots of the tree. And how much closer to the tree trunk cutting at the property line is.
I have a white spruce tree near the property line, and my neighbor cut two of its encroaching roots on the west side, each four inches in diameter and six feet from the trunk. This was about ten years ago when the tree was thirty-five feet high. The prevailing winds here are from the NW in the winter, SW in the summer. The tree is now fifty feet high, no impact.
My point is that roots will grow 1-3ft a year if they want to, and if you cut just around your bed(s), it will be an every year or every other year process if you want to keep roots out completely. Additionally, if you dig and loosen the soil, that makes the soil environment especially yummy for root growth, and they will grow back that much faster.
Your tree in question is 20ft from the property line, mine is 6ft, but your going to have to make your own decision. It's a myth that roots only grow within the tree canopy's reach. Roots are opportunists and grow the most where the conditions are best. if your soil is better than your neighbor's, once the tree roots invade and discover same, the tree's roots are going to want to grow more in your yard than his. (Likewise, your raised beds are especially "attractive".) It's not uncommon for wild trees to grow three times the height of the tree on one side and less than height of the tree on the other.
If you want to deter roots from growing back, the easiest thing to do is when you have replaced the soil (the more clay-like, the better), get that soil wet, and stomp on it to remove as much air space from the soil as possible. When it dries, the more cement-like it is, the better, because it is least hospitable for root growth. Obviously, this will not impact anything growing in the raised beds, but if (for instance) you grow grass where you dig, the grass won't grow, either.