The development of beyond-CMOS technologies with alternative basis logic functions necessitates the introduction of novel design automation techniques. In particular, recently proposed computing systems based on memristors and bilayer avalanche spin-diodes both provide asymmetric functions as basis logic gates - the implication and inverted-input AND, respectively. This article therefore proposes a method by which Karnaugh maps can be directly applied to systems with asymmetric basis logic functions. A set of identities is defined for these memristor and spintronic logic functions, enabling the formal demonstration of the Karnaugh map method and an explanation of the proposed technique. This method thus, enables the direct minimization of spintronic and memristive logic circuits without translation to conventional Boolean algebra, facilitating the further development of these novel computing paradigms. Preliminary analyses demonstrate that this Karnaugh map minimization approach can provide a 28 percent reduction in step count as compared to previous manual optimization.