In my experience, mate as used to describe another human being essentially never refers to any kind of sexual activity or sexual partner. Mate means different things, depending on the locale and dialect, for instance:
Uses the word mate to mean singular you in many dialects of English, particularly Australian English and Cockney and Northern British English.
Now look here, mate
Is an intensified aggressive form of the word "you" in some dialects of British English
Me and my mates are going to go out later for drinks
What time are your mates going to get here?
Is an informal meaning of "friends", in many dialects of English, but particularly as spoken in Northern England.
Mate is also an older English title, meaning "member" or "partner" (in a non-sexual context), and this holds over in many seafaring and military contexts:
Capitan Silver, this is First Mate Johnny Williams.
In this context, mate and first mate are naval titles. You'll sometimes see this as well in the "Pirate Vernacular":
Ahoy there, mateys!
In this case, "mateys" is an old fashioned (and no longer grammatical) plural of mate, and is an address to the crew. It does not imply that the crew are either friends or sexual partners of the captain.
Finally, it is important to note that mate almost always does have a sexual context whenever the discussion is specifically about non-human animals. In this case it can be either a verb or a noun.
We're flying in Kanga to Sydney zoo to mate with Zippy the Kangaroo who lives there.
Penguins mate for life
Liara, the lioness at London Zoo is the mate of Rory the Lion
As we can see, the peacock spreads its tail features to attract a mate.
Do not use the word "mate" meaning a sexual partner in the context of another human being outside of the context of academic medical research. Doing so is very insulting, because it suggests that the partner is almost in-human, and suggests a coldness or clinicalness to the activity that your listeners would likely find uncomfortable.