Changing sim cards

If I change my sim card to others iqama, can I use my tawakkalna and absher with the same sim until my exit visa?

Change your SIM to prepaid.  Much easier.  When you exit and don't recharge, SIM will eventually expire.

I would avoid doing what you are suggesting.  Mobile number, nowadays in Saudi, is your identity.  Anyone who receives OTP for your accounts, can literally do anything to you.

No issue of privacy. I would like to change sim to wife iqama. Is it applicable for use my tawakkalna and absher after changing.

Theoretically yes - it used to work but with the changes in the system that they are doing, I wouldn't be surprised if they match mobile number with Absher registered number and your account gets blocked.   Nowadays, they are issuing new SIMs by making you give them OTP through CITC website while sitting in Mobily / STC offices to prevent just this kind of misuse.