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The extension of uniform Schengen visa in the territory of the Slovak Republic is basically not possible.

EXCEPTIONS: in exceptional cases, the period of validity of your visa may be extended by maximum three months within one half-year. The application for a visa validity extension must be submitted at the competent Foreign Police Department. 

If your uniform Schengen visa validity is to expire and you do not have a Slovak residence permit you must leave the territory of the Slovak Republic. You may apply for a new visa abroad.

The visa application to enter the territory of the Slovak Republic along with the supporting documents is submitted on an official application form at the Diplomatic Mission or Consulate of the Slovak Republic abroad.

In exceptional cases, the Police Unit may issue the visa at border crossing points if the applicant fulfills certain conditions, i.e. the applicant was unable to apply for a visa in advance and submits, if required, supporting documents proving unforeseeable and imperative reasons for entry. Equally, the applicant must have a valid travel document, justify the purpose and conditions of the planned stay, have sufficient financial means for living expenses during the planned residence and return to the country of origin, eventually must be able to acquire such financial means lawfully. Such visa entitles the holder to stay for a maximum duration of 15 days.

Pursuing to an international agreement, a visa may be issued by a Diplomatic Mission or Consulate of another EU member state abroad.

You may find out more here.

Warning: There is no legal entitlement to be granted a visa, aside from visa granted to a family member of an asylum seeker, fulfilling the conditions pursuant to Act No. 480/2002 Coll. on Asylum. The foreign national will not be informed of the reasons for visa revocation.