In recent years, DNA has been regarded as a reliable raw material for building biological computers and biochips due to its nanoscale size, ultralow energy consumption, and high-performance computing potential. As the basis of building a biological computer, the research on the construction of nanoscale logic arithmetic and nanoscale biochemical logic circuits based on DNA molecules as carriers has attracted increasing attention. Although researchers use DNA strand replacement systems to achieve it this requires adjustment and careful design of the toehold, making sequence selection more difficult. To reduce dependence on the toehold, we propose a 3-way DNAzyme complex composed of three E6 DNAzymes assembled using the biological characteristics of E6 DNAzyme. This complex enriched the recognition vector of E6 DNAzyme, which can be used for multiple substrates, thus improving the reusability and efficiency of DNA molecules. At the same time, based on the 3-way DNAzyme complex and without the involvement of the toehold, we designed logic gates such as the OR gate, the AND gate, and the INHIBIT gate, and realized the construction of a new half subtractor and nanoscale biochemical logic circuit. These explorations and attempts extended the practicality of the 3-way DNAzyme complex. We believe that these logic elements will have a wide range of applications in DNA nanoscale programming, biological computing, and nanoscale medicine.