Fill a large bowl halfway with cold water and squeeze in juice from 1/2 lemon. Working with 1 artichoke at a time, break off outer leaves at the base. Continue removing leaves until only innermost tender yellow leaves remain. Cut artichokes crosswise and discard prickly tips. Trim all but 1 in. of stem, then trim outer layer of stem and the base to remove any dark green bits. Put into lemon water.
Mix remaining 3 tbsp. lemon juice, the oil, salt, and pepper in a bowl. Working with 1 artichoke at a time, blot dry, then shave lengthwise with a mandoline or a vegetable peeler into the oil mixture.
Add arugula and mint to artichokes; toss to coat. Divide salad among plates, then shave cheese over each.