  Recent experimental and theoretical studies have established that the
spin-lattice relaxation rate, $1/T_1$, measured in nuclear magnetic resonance
(NMR) experiments is a site-sensitive probe for the electronic spectrum in the
mixed state of the high-$T_c$ cuprates. While some groups suggested that
$1/T_1$ is solely determined by spin-flip scattering of BCS-like electrons,
other groups stressed the importance of antiferromagnetic spin-fluctuations. We
show that these two relaxation mechanisms give rise to a {\it qualitatively}
different temperature and frequency dependence of $^{17}$O $1/T_1$. A
comparison of our results with the experimental $^{17}$O $1/T_1$ data provides
support for a relaxation mechanism dominated by antiferromagnetic
spin-fluctuations.
