Based on the latest design requirements proposed by the Beijing On-Line Isotope Separation (BISOL) project, a new ${\mathrm{Sn}}^{22+}$-based, 81.25 MHz CW radio frequency quadrupole (RFQ) with external bunching has been designed. This RFQ can accelerate ${\mathrm{Sn}}^{22+}$ to 0.5 MeV/u with an output longitudinal-normalized rms emittance of 0.20 keV/u·ns over a length of 5.6 m. The tolerance and error analysis results indicate that this RFQ can handle a wide range of non-ideal beams while maintaining relatively lower longitudinal emittance growth and higher transmission efficiency. To maintain the beam intensity, the RFQ will simultaneously accelerate three kinds of high-charge-state mixed ions (${}^{132}{\mathrm{Sn}}^{21+}$, ${}^{132}{\mathrm{Sn}}^{22+}$ and ${}^{132}{\mathrm{Sn}}^{23+}$), the simulation results given by Impact-T show that the RFQ can achieve high transmission of the mixed beam. Compared with the previous ${\mathrm{Sn}}^{21+}$-based internal bunching RFQ scheme, this RFQ has a shorter length and smaller output emittance, which is beneficial to the designs of subsequent Medium-energy Beam Transport (MEBT) and Drift Tube Linac (DTL). In electromagnetic design, a four-vane structure with 48 tuners and 16 $\pi$-mode stabilizers (PSLs) were chosen. The results of the multi-physics analysis show that the maximum temperature rise and the maximum deformation of the cavity are 13.6 K and 40.3 µm, respectively. The results simulated with CST Microwave Studio (CST) and HFSS software were consistent.