For a description of the particulars of a mzdový list, see https://portal.pohoda.cz/dane-ucetnictvi-mzdy/mzdy-a-prace/n...

I think we would normally use a simple “payroll record” or, my preference, “payroll sheet”.

UK government: “For each employee working for you on 6 April, you’ll need to:
• prepare a payroll record”
https://www.gov.uk/payroll-annual-reporting/update-employee-...

Consider also: “The records maintained by the employer about the number of hours worked, salaries and wages, bonuses and commissions, health and pension plans, sick pay and pension pay and finally deductions on the payroll for all the employees are called payroll records.”
https://www.mbaskool.com/business-concepts/human-resources-h...

The labour ministry has a glossary listing mzdový list as “tax card” https://portal.mpsv.cz/eures/podminky/dokumenty/slovnik/zobr... . However, Google Images indicates that a “(income) tax card” is literally a plastic card. Might be worth investigating the German “Lohnsteuerkarte” though.