Can CRISPR also remove DNA viruses?
Yes, this should in principle work, and a number of groups have shows that it works in cultured cells:


  We found that CRISPR/Cas9 introduced InDel mutations into exon 2 of the ICP0 gene profoundly reduced HSV-1 infectivity in permissive human cell culture models and protected permissive cells against HSV-1 infection.... Combined treatment of cells with CRISPR targeting ICP0 plus the immediate early viral proteins, ICP4 or ICP27, completely abrogated HSV-1 infection. We conclude that RNA-guided CRISPR/Cas9 can be used to develop a novel, specific and efficacious therapeutic and prophylactic platform for targeted viral genomic ablation to treat HSV-1 diseases.


--Inhibition of HSV-1 Replication by Gene Editing Strategy

There's also been at least one trial in an animal model:


  Using a hydrodynamics-HBV persistence mouse model, we further demonstrated that this system could cleave the intrahepatic HBV genome-containing plasmid and facilitate its clearance in vivo, resulting in reduction of serum surface antigen levels. These data suggest that the CRISPR/Cas9 system could disrupt the HBV-expressing templates both in vitro and in vivo, indicating its potential in eradicating persistent HBV infection.


--The CRISPR/Cas9 System Facilitates Clearance of the Intrahepatic HBV Templates In Vivo