It comes amid a wave of industrial action on the railways, which will also see RMT members working for ScotRail walk out on strike on Monday October 10.
On October 1 and October 8, ScotRail will run 379 trains – one more than it was able to put on during strike action in August.
While the rail operator usually runs about 2,150 services per day, over the next two Saturdays it will only run trains on 11 routes across the central belt, Fife, and the borders.
David Simpson, ScotRail service delivery director, said that the “vast majority” of services would not be running, resulting in “significant disruption”.
He said: “It’s really disappointing to see more widespread disruption across the whole Great Britain rail network at a time when we need to be encouraging more people back to the railway.
“For ScotRail, it’s going to mean that we won’t be able to operate the vast majority of our services, which we know will be really frustrating for our customers. ”
Mr Simpson added the knock-on effects of the industrial action would impact on services on both Sunday October 2 and Sunday October 9 as well.
ScotRail customers should expect significant disruption to services on Saturday October 1 and Saturday October 8, as well as on the following days,” he warned.
“We’re advising customers to seek alternative means of transport and to only travel if they really need to on the day of strike action.
“Customers should check your journey in advance to make sure your train is running if you’re travelling on the day following strike action, on Sunday October 2 and Sunday October 9.”
On both Saturday October 1 and Saturday October 8, ScotRail will be running two trains per hour on the following lines: Edinburgh Waverley to Glasgow Queen Street via Falkirk High; Edinburgh Waverley to Helensburgh Central; Glasgow Central to Hamilton/Larkhall; Glasgow Central to Lanark line; Edinburgh Waverley to Cowdenbeath line; Edinburgh Waverley to Tweedbank; Milngavie to Springburn .
One train per hour will be operating on the Edinburgh Waverley to Glasgow Central via Shotts line, the Edinburgh Waverley to Larbert line, the Glasgow Queen Street to Larbert line and the Glasgow Queen Street to Falkirk Grahamston line.
Services will run between 7.30am and 6.30pm, although ScotRail is warning travellers that the final services will run “well before” this time.