A: As the Trustee, you have a fiduciary responsibility to manage and protect trust assets, so it is good on you that you are wanting to take action. However, what you are able to do largely depends on the type of trust (revocable or irrevocable) and the explicit terms of the trust.
Generally, a revocable trust may be modified by the settlor at any time. So, if you are the trustee and also the settlor, you have the inherent authority to make modifications to the beneficiaries.
If it is an irrevocable trust, it may be modified with the consent of all parties (beneficiaries including the beneficiary that you want removed) or by order of the Court.