I would put it differently. TWOSTEP certainly allows ordinal variables, but it treats them the same as nominal variables. They are simply assumed to be multinomial. As ttnphns says, though, treating ordinal variables as continuous might be satisfactory Clustering is a rather ad hoc technique. You might also want to consider using a Support Vector Machine (SVM) in unsupervised mode via the STATS SVM extension command. That procedure distinguishes between ordinal and nominal scales, although unsupervised mode is mainly useful for anomaly detection.
You can install this extension from the Utilities menu in Statistics 22-23 or the Extensions menu in V24. It requires the R Essentials.