Diluting is never wrong!
With sulphuric acid you may consider to look for an adsorbant, but with conc. hydrochloric acid or conc. nitric acid you should hurry up to stop the creation of the caustic vapors. Consider that conc. nitric acid is also a strong oxidysing agent and may ignite several materials.
All these acids can be deactivated by adding water. Since the spilled acids will be found as a thin film on a surface the heat developed by diluting the acids with water is perfectly transmitted. So do not fear spraying or boiling of the liquids when you dilute with water. Even chlorosulphonic acid will react moderately although in this case a lot of hydrogen chloride is developed which may enforce you to have a breathing protection if the mishap occurred outside of a fumehood.
The diluted acids may be neutralised with sodium hydrogencarbonate. Just spread the solid material onto the puddle until no more foaming is observed. Then you may remove the resulting salt solution with a cloth or wipe it into a floor drain. Consider that a lot of effort is needed to get the surface salt free again. You will have to wipe several times.
Minor volumes may directly flushed down the drain. Rinse with plenty of water.