Use the save (reexported from Vega.jl) function from the FileIO.jl package to save plots.
For example, to save a plot named p, you can use the following type of code:
p |> save("figure.png")
p |> save("figure.svg")
p |> save("figure.pdf")
p |> save("figure.eps")
p |> save("figure.vega")