Governments always claim they have a mandate for their policies as specified in their manifesto. (They will also claim a mandate for policies conjured up subsequently for which they do not have a mandate!)
They do have a mandate as seen from definitions in dictionaries, etc. However these mandates are not democratic mandates since a majority of the electorate have voted for other parties and policies. These policies are commonly similar and so a majority have voted for alternative policies to those enacted by the government for which they claim a mandate. The government may win 45% of the vote (normally about this value), the next 2 or 3 parties with similar policies may have 40%, 10% & 5%.
This just reflects the nature of electoral systems which are not democratic, such as in the UK and USA. The elected representatives are said to have a mandate to support the policies of their party. However, the elected members are not representative of all their constituents, only those who voted for them. The other people cease to exist. Whether a vote is 10,000 to 9,999 or 10,000 to 0 only the 10,000 count.
The way voters are ignored/discounted can easily be shown, e.g. in the 2015 UK general election the SNP with 1.45 million votes had 56 MP’s the Liberal Democrats with 2.42 million had 8!
In the UK, a mandate simply reflects the quirk of an electoral system. It most commonly does not reflect a policy a majority of the electorate voted for or want.