I'm guessing your example data looks something like:

xs <- data.frame(aveCPM = 1:6, logFC = c(0.5, 10, -0.2, 0.1, -0.4, -2))

Then you can basically do this (you'll presumably want to drop the legend and fix the colours):

library(ggplot2)
library(dplyr)

xs %>%
    dplyr::mutate(
        out_of_bounds = abs(logFC) > 3,
        logFC = ifelse(out_of_bounds, 3 * sign(logFC), logFC)
        ) %>%
    ggplot(aes(x = aveCPM, y = logFC, shape = out_of_bounds)) +
    geom_point() +
    ylim(-3, 3)