When you use pip to install a package, all the required packages will also be installed with it (dependencies). Does uninstalling that package also remove the dependent packages?

No, it doesn't uninstall the dependencies packages. It only removes the specified package:

$ pip install specloud
$ pip freeze # all the packages here are dependencies of specloud package

figleaf==0.6.1
nose==1.1.2
pinocchio==0.3
specloud==0.4.5

$ pip uninstall specloud
$ pip freeze

figleaf==0.6.1
nose==1.1.2
pinocchio==0.3

As you can see those packages are dependencies from specloud and they're still there, but not the specloud package itself.

As mentioned below, You can install and use the pip-autoremove utility to remove a package plus unused dependencies.