On Monday, Scotland's First Minister and SNP leader, Nicola Sturgeon, confirmed she was going to seek parliamentary approval to call a fresh referendum on Scotland's independence.
Mundell said Wednesday it would be impossible to have a legal and decisive referendum on Scottish independence immediately after Britain's exit from the European Union (Brexit), as demanded by Sturgeon.
A second Scottish independence referendum could take place 18 months to two years from now, she said.
"Instead of playing politics with the future of our country the Scottish government should focus on delivering good government and public services to the people of Scotland. Politics is not a game".
She went on: "I will seek the approval of the Scottish Parliament to open discussions with the United Kingdom government on the details of a Section 30 order - the procedure that will enable the Scottish Parliament to legislate for an independence referendum".
Sturgeon said she's been trying to reach a Brexit compromise with Westminster, but has been met with a "brick wall of intransigence".
But Sturgeon and her supporters have argued the Brexit vote changed all that since Scotland voted for Britain to remain in the European Union by 62 per cent in the June 2016 referendum.
Sturgeon fought for having the United Kingdom remain in the single market, or sought an outcome that would at least allow Scotland to do so.
The comments come after an Ipsos MORI poll for STV News - of more than 1,000 respondents between 24 February and 6 March - found that Scottish people likely to vote were split 50/50 on the independence issue.
Sturgeon has said she wanted Scotland to have its own deal as part of the UK's Brexit agreement to maintain Scotland's access to the single market.
The UK Government conceded that the last referendum must be "made in Scotland", and they must honour that principle again - there should be no strings attached, no blocking mechanisms applied and no Downing Street diktat.
Brexit and May's commitment to pull Britain out of the single market are the reasons Sturgeon gave to justify seeking a second vote.
Scotland held its first referendum in 2014, when over 55 percent of the people voted against independence.
The First Minister added that the probable date of the referendum must be between the autumn of next year and the spring of 2019. It didn't say Monday whether it would do so, but said an independent ballot would be divisive.