No, probably not.
Given that the deceased gets a will-save to attempt to resist the initial attempt of Speak with Dead, I would think it would be conceivable to assume that the target is able to be subjected to a second will save. The plan may be flawed, however, as the target doesn't have to talk to you if it doesn't want to (they can respond by saying, "I refuse to answer that question.").
However, if you define a spirit being communicated with as Undead, then they are immune to mind-affecting spells, and are thus unable to be affected. Paizo.com defines Undead as being "once-living creatures animated by spiritual or supernatural forces." I think a RAW answerhard-line rule is going to be difficult to find considering that Speak With Dead doesn't specifically apply the Undead template to the target. The jump we are making to consider the target undead is operating under RAI (Rules as Intended), not RAW (Rules as Written).
Overall, I would say that it doesn't work considering a spirit of a deceased creature is probably considered undead, and therefore immune to mind-affecting spells.