Hidden sheets are not included when a spreadsheet is exported via getBlob. So you can temporarily hide any unwanted sheets prior to exporting.
function export() {
var ss = SpreadsheetApp.getActiveSpreadsheet();
var sheet = ss.getSheetByName('Unwanted Sheet');
sheet.hideSheet();
DriveApp.createFile(ss.getBlob());
sheet.showSheet();
}
The above only hides one sheet, which is enough in the context of your question. Here is a version that hides everything but one.
function exportSheet(sheetName) {
var ss = SpreadsheetApp.getActiveSpreadsheet();
var sheets = ss.getSheets();
for (var i = 0; i < sheets.length; i++) {
if (sheets[i].getSheetName() !== sheetName) {
sheets[i].hideSheet()
}
}
DriveApp.createFile(ss.getBlob());
for (var i = 0; i < sheets.length; i++) {
sheets[i].showSheet()
}
}