Here is a version without the plot loop using NaN at the breaks:
using Plots; gr()
x = -12:12
xp = [[i, i+1 - 5*eps(), NaN] for i in x[1:end-1]]
xx = collect(Iterators.flatten(xp))
yy = floor.(xx)
plot(xx, yy, c=:black, label=false, framestyle = :origin)
scatter!(xx', yy', msc=:black, mc=[:black :white :white], ms=3)