The Heavy Sieve can be crafted out of any of the Vanilla wood logs and will take on their texture accordingly.
Right-clicking the Heavy Sieve with a mesh will insert it. It can be retrieved by shift-right-clicking the block with an empty hand. Once a mesh has been inserted, the sieve can be right clicked with siftable blocks to sift them.
In Ex Nihilo Omnia, an Iron Mesh is required to sift blocks. Any lower level mesh will break instantly on use in a Heavy Sieve.
In Ex Nihilo Adscensio, any mesh will work, as meshes in Adscensio have no durability and only split the loot table.