Python matplotlib: connect two subplot diagrams

You can use the lines on your figure object. The advantage is that these figure lines are of higher level that the ones on axis, so no need to worry about drawing axis for it. (I got the idea from this stackoverflow answer: ref)

Applied to your code, this look like this:

import matplotlib.pyplot as plt
import matplotlib as mpl

#x-axis
x_axis = [0,1,2,3,4,5,6,7,8,19,20,21,22,23,24,25]

# Line 1
line = [99,91,86,80,80,76,72,72,73,74,76,78,79,80,80,80]


# create broken x-axis
f, (ax, ax2) = plt.subplots(1, 2, sharey=True)
ax.step(x_axis, line, color='red')
ax2.step(x_axis, line, color='red')

ax.set_xlim(0, 10.5)
ax2.set_xlim(18.5, 30)

ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)

ax2.spines['left'].set_visible(False)
ax2.spines['top'].set_visible(False)
ax2.spines['right'].set_visible(False)

ax2.tick_params(
                axis='y',
                which='both',
                left='off')

# seperators for x-axis

d = .015
kwargs = dict(transform=ax.transAxes, color='k', clip_on=False)
ax.plot((1 - d, 1 + d), (-d, +d), **kwargs) 

kwargs.update(transform=ax2.transAxes) 
ax2.plot ( (0-d ,0+d),(-d, +d ), **kwargs)

# transFigure: used to transform the coordinates from your subplots
# to coordinates on the figure
# points are hardcoded as an example
transFigure = f.transFigure.inverted()
# last point on your left figure
coord1 = transFigure.transform(ax.transData.transform([8,74]))
# first point on your right figure
coord2 = transFigure.transform(ax2.transData.transform([19,74]))

# generate your line with the transformed coordinates
line = mpl.lines.Line2D((coord1[0],coord2[0]),(coord1[1],coord2[1]),
                       transform=f.transFigure, color='red')
# add your line to the figure
f.lines.append(line)

plt.show()