Can you just do spell casting as a witch?

I assume you mean, just casting spells as compared to the additional rituals etc of Wicca. That is possible and there is nothing wrong with that. I will offer some tips for casting spells that it is good to keep in mind. 

What To Know To Cast A Spell

“To know others is Intelligence.
to know your self is True Wisdom.
To conquer others is Strength.
To conquer yourself is True Power.”

Know The Basics:

My first advice is do not dabble. Understand what majick is and the different ways to raise, focus and ground majickal energy. Know how to cast a majick circle. Know how to open a circle. Know the basic outline of a spell.

Know The Intent And Purpose:

What are you trying to accomplish? Do you want to: Heal someone’s illness? Ease your depression? Increase your concentration? Bring love into your life? Celebrate a sabbat? Honor the Goddess? Before you begin, know what outcome you are seeking. This helps prevents spells from having opposing repercussions from what was intended.

Know When To Cast The Spell:

Learn how the Moon phases can impact your majick. What kind of spell should you cast during the waning Moon? The waxing Moon? Learn what day of the week will affect your workings, so you can plan the best timing of your spell.

(All of this information is available online or in the popular witchcraft and wicca books.)

How To Break Or Correct A Spell

Use majickal tools that will represent protection, balance, centering, and perhaps an object from the original spell.
Be sure to cast your circle properly before practicing any majick ritual.

Chant:”On the Eve of date,
I cast a spell
The effects I created
I now must quell,
Specifically, what it is.
May this spell be lifted,
and I now be gifted
With what it should be.”

(This spell’s purpose is not to undo a majickal working that has negative repercussions. This does not ‘un-do’ a spell, it stops it from continuing, or alters it slightly. Remember the Threefold Law.)