Can Texas suspend my license if I received a DWI in another state?

No. Texas cannot suspend your license if you receive a DWI in another state, but it can, however, prevent you from applying for a Texas license during the period of suspension. 

It can also notify the state issuing your license of the Texas suspension and ask that the issuing state honor it.

Here, you should know that Texas and most other states belong to the Interstate Driver License Compact (kind of a treaty amongst the states), and if the issuing state is a Compact State, it will honor the Texas suspension. 

Lastly, it is improper for a law enforcement officer to seize a license issued by another state.