We report that crystalline 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA), an organic solid, is highly amenable to host divalent metal ions, i.e., Mg²⁺ and Ca²⁺, in aqueous electrolytes, where the van der Waals structure is intrinsically superior in hosting charge-dense ions. We observe that the divalency nature of Mg²⁺ causes never-reported unique squeezing deformation of the electrode structure, where it contracts and expands in different crystallographic directions when hosting inserted Mg-ions. This phenomenon is revealed experimentally by ex situ x-ray diffraction and transmission electron microscopy, and is investigated theoretically by first-principles calculations. Interestingly, hosting one Mg²⁺ ion requires the coordination from three PTCDA molecules in adjacent columns of stacked molecules, which rotates the columns, thus reducing the (011) spacing but increasing the (021) spacing. We demonstrate that a PTCDA Mg-ion electrode delivers a reversible capacity of 125 mA h g^-1, which may include a minor contribution of hydronium storage, a good rate capability of retaining 75 mA h g^-1 at 500 mA g^-1 (or 3.7 C), and stable cycle life. We also report Ca²⁺ storage in PTCDA, where a reversible capacity of over 80 mA h g^-1 is delivered.