Yes, in Texas a landlord can evict a tenant without stating a specific reason if there is no lease or the lease (written or oral) has expired. In those cases, the landlord may terminate a month-to-month or holdover tenancy by giving proper written notice, typically at least 30 days, unless the lease sets a different notice period.
However, if a fixed-term lease agreement is still in effect, the landlord generally must have legal cause (such as nonpayment of rent or a lease violation) to evict before the lease ends. In all cases, the landlord must obtain a court order and cannot use self-help eviction methods.
Read this handy guide on Texas eviction laws.
The information for this answer was found on our Texas Eviction Process answers.