An obvious implementation for zero(a::AbstractSparseArray) would be

zero(a::AbstractSparseArray) = spzeros(eltype(a), size(a)...)

However, in reality there's no specialization, and (the abstract fallback uses fill!:

In particular, that means that it will be filled with non-structural zeros.

The reason why I haven't sent the obvious pull request is that this change is backwards incompatible where it relates to object identity. Namely, a side-effect of using fill! is that for mutable objects, every zero has the same identity. Example:

julia> using SparseArrays

julia> y = zero(BigInt[1,2,3]); y[1] === y[2]
true

julia> y = zero(sparse(BigInt[1,2,3])); y[1] === y[2]
true

julia> Base.zero(a::AbstractSparseArray) = spzeros(eltype(a), size(a)...)

julia> y = zero(sparse(BigInt[1,2,3])); y[1] === y[2]
false

What do you think? Can we make this change in a minor release? If so, I'll gladly send in a pull request.