I don't think you can do that using the charts created on Dashboards.
However if you create the chart in Report itself and use that chart in Dashboard, you will have an option on that chart to show/hide the axis labels.
Edit the report chart -> Go to Formatting tab -> Uncheck 'Show Axis
Label' checkbox.
EDIT:
Show values
option comes when you create the chart in dashboard itself and not use the chart created on report. So you should first add a chart on your report(which you already have, based on the screenshot you added in the question) and then in your dashboard just add the report and use the same chart like this:
This is a snapshot of what I see when I edit the report chart(not dashboard chart).
Hope this will help.