Azure Site Recovery (ASR) supports exclusion of specific disks from replication when protecting either VMware VMs and/or Hyper-V VMs to Azure, using the Azure portal.

Protecting Azure VMs (Azure-to-Azure) does not support the exclusion of disks.

However, excluding a disk like this means that the disk will not exist at all in the target site, so will be missing from the VM on recovery. Therefore this is not an end-to-end solution for eg. Swap disks and Temp DB disks, as these do need to exist in the recovery site and need to be recreated manually.