'Mutual' is something you share, or is the same. You could say that we became friends through a mutual passion for music. Or if I am a friend of Anna's, and you are also a friend of Anna's, you can say that she is a mutual friend of ours.

'Reciprocal' is something which is returned. For example, two colleges could have a reciprocal arrangement with each other. College A lets students from College B use its facilities for free, and College B lets College A students do the same.

example:

I want to improve mutual relationship with that girl by constant reciprocal interaction.

We need to mutual cooperation to achive the goal. If I cannot reach your reciprocal response, sorry, that is hard to proceed out scheme.

Alexander, both of those words are synonyms. They both mean the same and they can be used interchangeably without problem.

If you look at the Thesaurus website, you can see they are within the first 3 synonyms for each other. That's pretty close.

http://www.thesaurus.com/browse/reciprocal
http://www.thesaurus.com/browse/mutual

And this is the definition for reciprocal:

http://dictionary.reference.com/browse/reciprocal

Hope it helps :)

It seems to me these two words are very similar. I would like to know in what context you would like to use these words. 

There is an idiom we use in America when one person likes another person, and the other person feels the same:

"i really like you."

"The feeling is mutual."

in in this case, the second person reciprocates the feelings of the first person. Here, mutual means the same as reciprocal.

You can also use the word "mutual" if you share the same friends as someone. "Unfortunately, my ex boyfriend and I have mutual friends." but here, reciprocle doesn't have the same meaning. you couldn't say "we have reciprocle friends."