In the finite element method (FEM), typical examples of multi-point constraints (MPCs) include rigid body couplings, tie constraints between non-conforming meshes, and periodic boundary conditions. Their robust enforcement is a recurring source of complexity in FEM implementations. Traditional FEM implementations follow a compute-assemble-solve paradigm based on manually derived weak forms and element-centric assembly routines. Within this framework, constraints are enforced by modifying the global system of equations, via DOF elimination, matrix transformations, or Lagrange multipliers, which often leads to complex implementations. Automatic differentiation (AD) has reduced the burden of deriving residuals and Jacobians, but it is commonly applied only at the element level. As a result, global assembly procedures and constraint handling still require manual implementation. In this work, we argue that modern AD frameworks (here JAX) can be applied directly at the global level by differentiating a discrete global functional with respect to all DOFs. This avoids explicit weak-form derivation and manual assembly, and enables a clearer separation between discretization and solution strategies. Building on this perspective, we present an approach for handling single- and multi-point constraints through automatic static condensation. The constrained problem is formulated by wrapping the functional in a mapping that depends only on free DOFs and computes constrained DOFs via the constraint equations. Differentiation of this reduced functional via global AD directly yields the condensed system of equations, without explicit derivation or implementation of condensation, transformation, or elimination procedures. This results in a simpler, more modular treatment of constraints.