To invoke HTTP methods in JMP Live, use Get HTTP Request():
lc = New JMP Live(Connection("JMP Live Connection"), Prompt(If Needed));
hrequest = lc << Get HTTP Request();
hrequest << URL(url);
hrequest << Method("GET");
data = hrequest << Send();
json_data = Parse JSON(data);
show(json_data);
For more details, see Communicate with REST Web Service.