Does dreaming cuts our sleeping hours? If I am dreaming a lot at night, how many effective hours am I sleeping at night?
After dreaming heavily at night, when I wake up in the morning I feel sluggish as if I haven't slept properly. 

Does dreaming cuts our sleeping hours?
One small study (2015)  in otherwise healty subjects, found no correlation between nightmares and the quality of sleep measured using widely used objective methods, or more precisely


  sleep measures obtained by ambulatory polysomnographic recordings revealed no group differences in (a) overall sleep architecture, (b) sleep cycle duration as well as REM density and REM duration in each cycle and (c) sleep architecture when only nights with nightmares were analyzed.


Nonetheless the subjects who experienced nightmares reported worse self-reported sleep quality. Granted, in a study like this, there's always a chance the authors failed to consider some objective sleep measure not commonly known/used today. Anyhow, the author's' conclusion was that


  nightmares result in significant impairment which is independent from disturbed sleep architecture


And thus they suggest one seek specialized treatment for nightmares... which are correlated with quite a few psychiatric disorders, PTSD, anxiety, depression, or borderline personality disorder, to name a few.

Another caveat of this study is that the authors deliberately excluded people with diagnosable psychiatric conditions from the sample. So this study does not exclude the possibility that subjects with (say) PTSD actually do have worse objective sleep... owing to nightmares.