how to fix the speed control of mixer kenwood a701 a?

Take it apart and have a good look at it - try to work out in your mind how it works... Give it a good clean - it may be chocked up with fine powder - flour or icing sugar.

Check out this recent answer...
http://howtomendit.com/answers.php?id=498669

Clean the contacts - check the resistor - replace the capacitor (pennies).

Good luck...
December 2014