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1.
A strange form of masturbation involving squatting on the ground with flat feet with your knees held tighly to your chest. You arm must then go around one of your legs to reach the required organ.

Often done furiously and sometimes in public
I`m off to the park for a Mexican Handshake
 
2.
Hand job + hot sauce = Mexican Handshake
It is customary to end an interview with a firm handshake. Note: a Mexican Handshake will severely reduce one's chances of landing the desired job. Unless the interviewer is into that sort of thing.
by Amateur Dentist December 17, 2009
 
3.
the act of greeting someone by grabbing and shaking one's croutch
After a long separation, Paco quickly greeted me with a mexican handshake.
by TiC_ToK September 27, 2004