Manual:$wgBlockDisablesLogin

Details
If set to "true", blocked users will no longer be allowed to login.

At runtime, any extra rights blocked users might have are removed as well (which is relevant, when the blocked user has a pre-existing session).

Also, if he is logged in, the user gets logged out.

Note
When using this with a public wiki allowing to edit via IP addresses, the effect of logging out blocked users may actually be adverse; unless the user's IP address is also blocked (e.g. autoblock), logging the user out will again allow reading and editing, just as for anonymous visitors.

Alternative
An alternative to this setting might be using  with   to create a group that revokes certain rights.