How is the concept of species defined in asexual organisms?
There is no taxonomic category called "asexual organism". It is rather a phenotypic trait of scattered occurrence. 

However the absence of sexual-reproduction in a group of organisms sometimes causes problems in scientific classification. This caused development of the artificial-group fungi-imperfecti (or deuteromycota) at one time, for fungal strains which lack sexual reproduction. 

Bacteria and archaea (prokaryotes) are not known to show sexual reproduction. However  they  show  some gene transfer processes like conjugation and transformation; but this is not the same as sexual reproduction because cell fusion does not take place.