to render someone speechless can mean to leave someome with nothing to say.
Make me speechless or leave me speechless is what one may say to another person asking the other person to surprise him/her.
The statement "leave me/one speechless" means to shock someone, or surprise someone to the point that they have nothing to say.
It could be both a bad and a good message, but it relies heavily on the in context.
Also use in place of awe, or overwhelmed. Again, depending on the context.
-PEACE