For thy face coins them, and thy stamp they bear,
And by this mintage they are something worth
The speaker of the poem, in these lines, is telling the lover that the tears he/she pours for him/her are only valuable (have meaning) because they are shed in front of him/her at this moment of separation. The tears are something worth because of the moment and the lover who coins them.
Draw not up seas to drown me in thy sphere
In this line, the speaker of the poem, is asking of the lover to not weep too much because the sight of the tears is too much to bear. It may also be interpreted as a warning to not cry so much, for he/she is not dead yet, and too much mourning might foreshadow death; hence, in the next line the speaker says "weep me not dead".
Whoe'er sighs most is cruellest, and hastes the other's death.
This is a paradoxical statement - not a rare occurrence in Donne's poetry. Similar expression is presented in another one of his poems called "Sweetest love, I do not go" and it states that the sighing for a lover, an act out of love, is cruel and deadly for the recipient. The lovers breathe as one and the grief that one feels is devastating to the other.