Is it wrong if I cluster numerical attributes and categorical attributes separately?
Generally, clustering on separate categorical and numerical features is wrong since it could lead to merging the otherwise separate clusters. Here is a visual example of why this may fail (drawn by myself):



If we cluster only on the categorical feature, clusters C1 and C2 would be merged. If we cluster only on the numerical feature, all three clusters would be merged. Therefore, clusters C1 and C2 could not be found separately.

As a side note, this blind separation is different than a careful feature selection (mentioned in this answer) which could end up with both categorical and numerical features.