That depends whether the employee is on a full time or part time contract.
Basically, three options for employees on full time indefinido contract.
An employer can propose a new contract with less hours, but the employee(s) are entitled to refuse if they don´t agree. They cannot be dismissed for refusing to agree with your proposal to decrease working hours.
Second option would be to add an ERTE clause to the existing contract, as an addendum. ERTE stands for ´Expediente de regulación temporal de empleo´ and it allows you to temporarily decrease the number of hours a certain employee or several or all employees work, for a limited period of time. Decrease of hours should be between 10 and 70% of their fulltime contract, and can be in hours/day, days/month or even a certain period in the year. If the employee has built up entitlement to unemployment benefits, she can apply for paro for the hours she isn´t working for you, temporarily.
For the employer, if you maintain the employee on contract for at least 12 months after the ERTE has ended, a bonification of 50% of the Seguridad Social contributions during the ERTE can be applied for.
I suggest to consult an accountant or gestor laboral for the details as you have to follow a precise procedure for the measure to stand in social court, should the employee decide to appeal. It´s outlined in article 47 of the Estatuto de Trabajadores. http://noticias.juridicas.com/base_datos/Laboral/561075-et-2015.html#a47
Third option would be to dismiss the employee, but for objective reasons, technical, economical, organisational or productional. And pay indemnization of course. For it to stand if appealed, refusing to sign the new part time contract cannot be the reason and if you claim it´s for economical reasons, you cannot employ someone else in her stead as this would give her grounds to appeal.
For employees on a part time contract, it is possible to permanently decrease the amount of hours without prior consent, but the employer must justify this in writing and for it to stand up against an appeal it should be for economic, technical, organisational or productional reasons. If you want to appeal your employer´s decision, please contact a professional in labour law to help you with this, e.g. from a worker´s union.
The option of an ERTE as described above, is valid for those on part time contracts also.