Strand displacement technology and ribozyme digestion technology have enriched the intelligent toolbox of molecular computing and provided more methods for the construction of DNA logic circuits. In recent years, DNA logic circuits have developed rapidly, and their scalability and accuracy in molecular computing and information processing have been fully demonstrated. However, existing DNA logic circuits still have some problems such as high complexity of DNA strands (number of DNA strands) hindering the expansion of practical computing tasks. In view of the above problems, we presented a toehold preemption mechanism and applied it to construct DNA logic circuits using E6-type DNAzymes, such as half adder circuit, half subtractor circuit, and 4-bit square root logic circuit. Different from the dual-track logic expressions, all the signals in the circuits of this study were monorail which substantially reduced the number of DNA strands in the DNA logic circuits. The presented preemption mechanism provides a way to simplify the implementation of large and complex DNA integrated circuits.