We propose a mechanism whereby the intense, sheet-like structures naturally
formed by dynamically aligning Alfv\'enic turbulence are destroyed by magnetic
reconnection at a scale $\hat{\lambda}_{\rm D}$, larger than the dissipation
scale predicted by models of intermittent, dynamically aligning turbulence. The
reconnection process proceeds in several stages: first, a linear tearing mode
with $N$ magnetic islands grows and saturates, and then the $X$-points between
these islands collapse into secondary current sheets, which then reconnect
until the original structure is destroyed. This effectively imposes an upper
limit on the anisotropy of the structures within the perpendicular plane, which
means that at scale $\hat{\lambda}_{\rm D}$ the turbulent dynamics change: at
scales larger than $\hat{\lambda}_{\rm D}$, the turbulence exhibits
scale-dependent dynamic alignment and a spectral index approximately equal to
$-3/2$, while at scales smaller than $\hat{\lambda}_{\rm D}$, the turbulent
structures undergo a succession of disruptions due to reconnection, limiting
dynamic alignment, steepening the effective spectral index and changing the
final dissipation scale. The scaling of $\hat{\lambda}_{\rm D}$ with the
Lundquist (magnetic Reynolds) number $S_{L_\perp}$ depends on the order of the
statistics being considered, and on the specific model of intermittency; the
transition between the two regimes in the energy spectrum is predicted at
approximately $\hat{\lambda}_{\rm D} \sim S_{L_\perp}^{-0.6}$. The spectral
index below $\hat{\lambda}_{\rm D}$ is bounded between $-5/3$ and $-2.3$. The
final dissipation scale is at $\hat{\lambda}_{\eta,\infty}\sim
S_{L_\perp}^{-3/4}$, the same as the Kolmogorov scale arising in theories of
turbulence that do not involve scale-dependent dynamic alignment.