Definitely yes, you can perform cluster analysis on ordinal data.
As about the clustering methods probably the best approach is to choose a Latent Class clustering (with Latent Gold for example).
Hierachical clustering at the respondent level is also a commonly used method.
But you have to compute the Canberra proximity (recommended for ordinal data) between respondents and then you can use this matrix as input for the SPSS hierachical cluster analysis (see Cluster command with Matrix IN).
In a similar way for a much more general case when you have a combination of variables with scale, nominal, ordinal and binary structure you can use the Gower proximity (similarity) measure as input for Cluster command in SPSS.
Unfortunately both proximity measurements are not available for the moment in the SPSS package but there are many other tools that might help you to calculate them.
Hope it helps!
.... impossible is nothing ....
"..Singularities are typically hidden within event horizons, and therefore cannot be seen from the rest of spacetime..."