Biomineralized lattice materials with have high mineral contents (~ 99 wt%), usually "conceal" multiscale structural arrangements for unique mechanical or functional performance, such as the remarkable damage tolerance despite of the brittle nature of the constituents (e.g., biogenic silica and calcite). However, the quantitative explorations of the structure-mechanics relationships in multiscale of biomineralized lattices remain insufficient and hence hinder the leverage of the functional benefits to design architected cellular materials. In this dissertation, I selected two groups of marine animals (i.e., Hexactinellid sponges and Echinoderms) for systematic structural-mechanical study. Their biomineralized lattice skeletons exhibit three representative types of multiscale structures: 1) multiscale hierarchical structure: skeleton of Hexactinellid sponge such as Euplectella aspergillum; 2) multiscale functionally graded structure: spine of sea urchin Heterocentrotus mammillatus; and 3) dual-scale (atomic and microlattice scales) periodic structure: ossicle of starfish Protoreaster nodosus. This dissertation develops quantitatively the structural-mechanical/functional correlations in biomineralized cellular materials for bio-inspired material design. Four different species of Hexactinellid sponges have been studied with particular focus on the species E. aspergillum. As an example of the multiscale hierarchical biomineralized lattice, the extremely lightweight skeleton (~99% porosity) of E. aspergillum exhibits 1) amorphous nanoparticular biogenic silica; 2) micron-sized fibrous spicule with cylindrically laminated silica layers separated by organic interfaces; 3) spicule bundles where the individual spicules merged by secondary silica deposition; 4) a centimeter-sized Voronoi-like cellular dome known as sieve plate; and 5) a centimeter-sized cylindrically arranged rectangular lattice with double-diagonal reinforcement and external helical ridge. Here, we discovered a series of mechanical or functional properties or formation process of structures in different length scales: 1) for the biogenic silica in three different species of Hexactinellid sponge, consistent modulus and hardness of the biogenic silica throughout the cross section of the spicule are found via substantial correlation between the measured values and locations; 2) for the sieve plate, the Voronoi-like cellular dome constructed by porous branch with increased height achieves balance between improved mechanical stiffness and large pore opening for sponge's current pumping mechanism; 3) via microstructural study, the formation process of the sieve plate is proposed; and 4) for the cylindrical skeletal body, the double-diagonal configuration and the ridge structure are found to provide tendency to optimize torsional rigidity, and enhanced radial stiffening and improved permeability, respectively. The cellular structure in the spine of the H. mammillatus (i.e., stereom) made of ~99wt% of single-crystalline calcite shows a multiscale functionally graded structure. We developed and optimized a cellular network analysis workflow on the large-volume 3D lattice structure obtained from the synchrotron-based micro-Computed Tomography scan. The analysis provides quantitative descriptions of the branch, ring structure, and septum which reveals a functionally graded structure in multiscale from the center region to the edge region of the spine: 1) in microscale, the branch thickness and length increases, resulting in a significantly decreased porosity; and 2) in macroscale, the center region of the spine with galleried stereom of highly aligned branches transits to the edge region with laminar stereom of radially arranged septa and interconnecting branches. The multiscale structural variations lead to the mechanical variations the increased elastic modulus and mechanical isotropy from the center to the edge of the spine. This provides a biological pathway for designing the lightweight, strong, and tough beam with multiscale structural gradient. In previous work, we discovered that ossicle in starfish P. nodosus possesses a unique dual-scale periodic lattice structure, which means periodic single crystal calcite in nanoscale and diamond triply periodic minimal surface (diamond-TPMS) lattice in microscale. It has three unique structural features: 1) microlattice dislocations in ossicles similar to those found in crystals with diamond cubic lattice; 2) a diamond-TPMS microlattice with ca. 50% relative density; and 3) dual-scale crystallographic coalignment between c-axis of the single-crystalline constituent calcite and the [111] direction of the diamond-TPMS microlattice. Based on this work, this dissertation mainly reveals: 1) unique type and core structures of the dislocations in the ossicle for stiffness, strength, and toughness; 2) the 3D property compensation of dual-scale crystallographic coalignment for improved mechanical isotropy; and 3) mechanical benefits (improved mechanical isotropy and effective fragment jamming) and morphological benefits (minimal surface and highest surface area to volume ratio) for 50% relative density. / Doctor of Philosophy / Architected lattice materials, featured by their tailorable 3D multiscale architectures, achieve unique mechanical properties such as breaking the trade-off between strength and toughness, and mechanical isotropy reaching theoretical limit. In nature, as a result of evolutionary driving force, the biomineralized skeletons of the animals such as sea sponge, sea urchin, and starfish usually delicately control the architectural arrangements in different length scales and provide excellent templates for the design of architected lattices with desirable properties. Quantitative understanding of the 3D multiscale structures and mechanics of these natural biomineralized lattices allows the development of bio-inspired materials that are, for example, simultaneously stiff, strong, and tough. This dissertation establishes the quantitative structural-mechanical/functional relationships in multiscale of three biomineralized lattices with high mineral contents (~99 wt%) and a wide range of porosity (50~99 vol%) in Hexactinellid sponges with main emphasis on species (Euplectella aspergillum), sea urchin Heterocentrotus mammillatus, and starfish Protoreaster nodosus. They are selected for their representative multiscale structures, i.e., multiscale hierarchical structure, multiscale functionally graded structure, and dual-scale (i.e., atomic and microlattice scales) periodic structure, respectively. Study of these biomineralized lattices significantly improve our understanding of the biological strategies in structural arrangement and pave the way towards bio-inspired modeling to leverage the mechanical benefits.