I am confused of 见笑，笑话 and 嘲笑。
他见笑/笑话/嘲笑我， can I say like this? they are the same meaning?
见笑 [jiàn xiào] - literally means to see a joke. Or to make a joke out of yourself.
让你见笑了[ràng nǐ jiàn xiào le] means “I’ve embarrassed myself in front of you”. It is often used as a self humbling way to respond to a compliment. If you are responding to a compliment, this would mean “I’m not that good. I’ve embarrassed myself.”
笑话 [xiào huà] - means
(1) a joke. We can add a verb in front 讲笑话 [ jiǎng xiào huà] to mean “to tell a joke”.
让你看笑话了 [ràng nǐ kàn xiào huà le] means the same as the usage with 见笑.
他是个笑话 [tā shì gè xiào huà] means “he is a joke.” So we can use this to insult someone.
(2) to make fun of.
You must be kidding. Mostly people say it with a casual tone.
嘲笑 [cháo xiào] - means “to make fun of” or “to ridicule”. This is an action.
他嘲笑我 [tā cháo xiào wǒ] means “he made fun of me.”
So, literally, yes they have the same meaning. But the context that fits these three is totally different.