Save a ggplot2 time series plot grob generated by ggplotGrob

library(tidyverse)
library(lubridate)
library(scales)

set.seed(123)
df <- tibble(
  date = as.Date(41000:42000, origin = "1899-12-30"), 
  value = c(rnorm(500, 5), rnorm(501, 10))
)

# create year column for facet
df <- df %>% 
  mutate(year = as.factor(year(date)))

p <- ggplot(df, aes(date, value)) + 
  geom_line() + 
  geom_vline(xintercept = as.numeric(df$date[yday(df$date) == 1]), color = "grey60") + 
  scale_x_date(date_labels = "%b", 
               breaks = pretty_breaks(),
               expand = c(0, 0)) +
  # switch the facet strip label to the bottom
  facet_grid(.~ year, space = 'free_x', scales = 'free_x', switch = 'x') +
  labs(x = "") +
  theme_bw(base_size = 14, base_family = 'mono') +
  theme(panel.grid.minor.x = element_blank()) + 
  # remove facet spacing on x-direction
  theme(panel.spacing.x = unit(0,"line")) +
  # switch the facet strip label to outside 
  # remove background color
  theme(strip.placement = 'outside',
        strip.background.x = element_blank())
p

ggsave("plot.png", plot = p, 
       type = "cairo", 
       width = 11, height = 8.5, units = "in", 
       dpi = 150)

Using theme_classic()

p <- ggplot(df, aes(date, value)) + 
  geom_line() + 
  geom_vline(xintercept = as.numeric(df$date[yday(df$date) == 1]), color = "grey60") + 
  scale_x_date(date_labels = "%b", 
               breaks = pretty_breaks(),
               expand = c(0, 0)) +
  # switch the facet strip label to the bottom
  facet_grid(.~ year, space = 'free_x', scales = 'free_x', switch = 'x') +
  labs(x = "") +
  theme_classic(base_size = 14, base_family = 'mono') +
  theme(panel.grid.minor.x = element_blank()) + 
  # remove facet spacing on x-direction
  theme(panel.spacing.x = unit(0,"line")) +
  # switch the facet strip label to outside 
  # remove background color
  theme(strip.placement = 'outside',
        strip.background.x = element_blank())
p

Add the top and right most borders

ymax <- ceiling(1.1 * max(df$value, na.rm = TRUE))
xmax <- max(df$date, na.rm = TRUE)

p <- ggplot(df, aes(date, value)) + 
  geom_line() + 
  geom_vline(xintercept = as.numeric(df$date[yday(df$date) == 1]), color = "grey60") + 
  scale_x_date(date_labels = "%b", 
               breaks = pretty_breaks(),
               expand = c(0, 0)) +
  # switch the facet strip label to the bottom
  facet_grid(.~ year, space = 'free_x', scales = 'free_x', switch = 'x') +
  labs(x = "") +
  theme_classic(base_size = 14, base_family = 'mono') +
  theme(panel.grid.minor.x = element_blank()) + 
  # remove facet spacing on x-direction
  theme(panel.spacing.x = unit(0,"line")) +
  # switch the facet strip label to outside 
  # remove background color
  theme(strip.placement = 'outside',
        strip.background.x = element_blank()) +
  ### add top and right most borders
  scale_y_continuous(expand = c(0, 0), limits = c(0, ymax)) +
  geom_hline(yintercept = ymax) +
  geom_vline(xintercept = as.numeric(df$date[df$date == xmax])) +
  theme(panel.grid.major = element_line())
p

^{Created on 2018-10-01 by the reprex package (v0.2.1.9000)}