So try to better explain this.
In general relativity, the dimensions space and time are connected, weaved together, forming a fabric, called space-time. anything in space time warps this fabric, this is what we perceive as gravity. And objects which warp space contract it, causing nearby objects to fall inward.
Negative mass, if it existed, is assumed to do the opposite-expand space, causing nearby objects to fall outward, or be repelled. Hence gravitational repulsion.
If you have two positive masses then the two contraction curvatures add up to one bigger contraction curvature, aka more positive gravity.
If you have two negative masses, then the two expansion curvatures add up to one bigger expansion curvature, aka more negative gravity.
*However, if you have both positive and negative mass near each other, the warping of space causes by both masses is equal(equal amounts of positive and negative mass), then the contraction and expansion of space will interact with one another, canceling each other out, creating a fabric with no space-time curvature, in other words, a region devoid of gravity. Thus negative mass would provide gravitational shielding as well.
How such masses operate and could be used for spacecraft propulsion are gone into more detail by propulsion physicist Marc Millis, in his book Frontiers of propulsion space flight.
There are 3 types of mass (for this discussion anyway). 3 concepts: inertial, passive gravitational, and active gravitational. Inertial mass is the resistance of objects to changes in motion, passive gravitational mass is the extent to which an object responds to gravity, active is the field which produces gravity, the charge of gravity, analogous to electric charge. All these masses are equivalent and inseparable, known as the Equivalence principle. If negative mass exists, it is assumed to not violate such a principle and thus possess negative mass in all 3 aspects.
There are two types of negative mass formulated over the years. One type is always negative (it repels itself and all positive masses). This type repels positive mass while the positive mass attracts The negative mass. They move together in a line. The 2nd type has positive mass when interacting with other negative mass, (the two masses attract) but when interacting with positive mass is negative, aka the two masses repel each other.
Assuming you had some way (note: insert technobabble) of producing enough negative mass, you would have a form of matter that gravitationally repels positive matter. A conductor is a device that contains equal positive and negative electric charges that shield any flow of internal electric charge from any electric charge outside it.
Thus, analogous electric charges, positive mass is positive gravitational charge, negative mass is negative gravitational charge. In addition, gravity radiates outwards as a sphere, but the presence of other masses distorts this gravity region, creating more of a bubble. A ring of negative matter around a spaceship would generate negative gravity, aka antigravity, aka gravitational shielding. The bubble of negative gravity generated would shield anything inside it from any gravity outside it. – Shaquille Nelson 2 days ago
Inside the bubble is a spaceship, outside is the Earth, and the Earth's gravity has been negated. In addition, the only gravity affecting the spaceship is the bubble of negative gravity. Remember, regardless of what type of negative mass you are using it gravitationally repels matter. Thus, this negative mass, if moved, will also move the spaceship, producing thrust without rockets. How you move the negative mass can be done using gravity fields or gravitomagnestism(or some other unknown way). If you can create any amount/density of negative matter. Then you can create any level of speed.
Thus, such a propulsion method would both negate Earth's gravity, eliminating the need to attain orbital velocity, AND produce thrust without rockets.