Hoeing it probably helps spread the seeds. The best thing you can do is carefully hand pull it. It is a spreading ground cover, so one plant covers a lot of space, so it takes less pulling than you might think. Find where the roots are and carefully dig them out. Then trash them! Even if the plant has no seeds at the time, it can ripen seeds up after it is pulled. Put the plants in a plastic bag and put in the trash. Then cover the cleared area with cardboard or heavy mulch. The purslane seeds can stay viable in the soil for years, but they need light to germinate. So keeping the soil covered helps prevent new seeds from germinating. No till methods help. Any time you till the ground you are bringing new purslane seeds up into the light to sprout.
Incidentally, you know it is edible? Very nutritious -- lots of vitamins A, C, and E and minerals and anti-oxidants and more omega 3's than any other leafy vegetable. And unlike many of what are called edible weeds, it is quite tasty, with some lemony overtones. I have a purslane potato salad recipe that I really like. So don't trash it, eat it!
