No, moderators cannot effectively suspend other moderators (it's impossible in chat, it simply doesn't do anything and the moderator can unsuspend themselves on the main site), neither in chat nor on the main sites. In a case where that is necessary, a Stack Exchange community manager or developer has to step in and remove the diamond from the offending moderator.
In most cases, this should not be necessary. As long as the moderator is willing to listen, just asking them to stop the problematic behaviour should be sufficient.
In cases where this doesn't work, an SE employee will have to clean up the mess. It would show a lack of judgement on the part of the moderator if this were necessary, and they probably wouldn't stay moderator if this happened (and can't be explained e.g. by someone else getting on their computer).
The important part is that some CMs can remove diamonds, and after that the moderator is just a regular user. There is no special suspension for moderators, if the need arises to suspend them, they have to lose moderator status.
