Yes a dentist can pull out an infected tooth but unless the infected tooth is considered an emergency and needs pulled right away the dentist will try using some antibiotics or other treatments to help cure the infected tooth.
Pulling any tooth including an infected tooth should be the last resort and dentists don't want to pull someone's tooth or teeth unless absolutely necessary.
First when you go to the dentist you'll have your teeth or tooth looked at and then an X ray of the teeth will be done to see where the infection is at.
Then a few days to a week or so later you'll have another dentist appointment where they will either pull the tooth if needed or continue with antibiotics.
If you want it pulled though then you can specify that and the dentist will pull the tooth if you really want it pulled.